Which journals publish expository work? I wonder if anyone else has noticed that the market for expository papers in mathematics is very narrow (more so than it used to be, perhaps).
Are there any journals which publish expository work, especially at the "intermediate" level?  By intermediate, I mean neither (i) aimed at an audience of students, especially undergraduate students (e.g. Mathematics Magazine) nor (ii) surveys of entire fields of mathematics and/or descriptions of spectacular new results written by veteran experts in the field (e.g. the Bulletin, the Notices).
Let me give some examples from my own writing, mostly just to fix ideas.  (I do not mean to complain.)

*

*About six years ago I submitted an expository paper "On the discrete geometry of Chicken McNuggets" to the American Mathematical Monthly.  The point of the paper was to illustrate the utility of simple reasoning about lattices in Euclidean space to give a proof of Schur's Theorem on the number of representations of an integer by a linear form in positive integers.  The paper was rejected; one reviewer said something like (I paraphrase) "I have the feeling that this would be a rather routine result for someone versed in the geometry of numbers."  This shows that the paper was not being viewed as expository -- i.e., a work whose goal is the presentation of a known result in a way which will make it accessible and appealing to a broader audience.  I shared the news with my officemate at the time, Dr. Gil Alon, and he found the topic interesting.  Together we "researchized" the paper by working a little harder and proving some (apparently) new exact formulas for representation numbers.  This new version was accepted by the Journal of Integer Sequences:

https://cs.uwaterloo.ca/journals/JIS/VOL8/Clark/clark80.html
This is not a sad story for me overall because I learned more about the problem ("The Diophantine Problem of Frobenius") in writing the second version with Gil.  But still, something is lost: the first version was a writeup of a talk that I have given to advanced undergraduate / basic graduate audiences at several places.  For a long time, this was my "general audience" talk, and it worked at getting people involved and interested: people always came up to me afterward with further questions and suggested improvements, much more so than any arithmetic geometry talk I have ever given.  The main result in our JIS paper is unfortunately a little technical [not deep, not sophisticated; just technical: lots of gcd's and inverses modulo various things] to state, and although I have recommended to several students to read this paper, so far nothing has come of it.


*A few years ago I managed to reprove a theorem of Luther Claborn (every abelian group is isomorphic to the class group of some Dedekind domain) by using elliptic curves along the lines of a suggestion by Michael Rosen (who reproved the result in the countable case).  I asked around and was advised to submit the paper to L'Enseignement Mathematique.  In my writeup, I made the conscious decision to write the paper in an expository way: that is, I included a lot of background material and explained connections between the various results, even things which were not directly related to the theorem in question.  The paper was accepted; but the referee made it clear that s/he would have preferred a more streamlined, research oriented approach.  Thus EM, despite its name ("Mathematical Education"), seems to be primarily a research journal (which likes papers taking new looks at old or easily stated problems: it's certainly a good journal and I'm proud to be published in it), and I was able to smuggle in some exposition under the cover of a new research result.


*I have an expository paper on factorization in integral domains:
http://alpha.math.uga.edu/~pete/factorization.pdf
[Added: And a newer version: http://alpha.math.uga.edu/~pete/factorization2010.pdf. ]
It is not finished and not completely polished, but it has been circulating around the internet for about a year now.  Again, this completely expository paper has attracted more attention than most of my research papers.  Sometimes people talk about it as though it were a preprint or an actual paper, but it isn't: I do not know of any journal that would publish a 30 page paper giving an intermediate-level exposition of the theory of factorization in integral domains.  Is there such a journal?
Added: In my factorization paper, I build on similar expositions by the leading algebraists P. Samuel and P.M. Cohn.  I think these two papers, published in 1968 and 1973, are both excellent examples of the sort of "intermediate exposition" I have in mind (closer to the high end of the range, but still intermediate: one of the main results Samuel discusses, Nagata's Theorem, was published in 1957 so was not exactly hot off the presses when Samuel wrote his article).  Both articles were published by the American Mathematical Monthly!  I don't think the Monthly would publish either of them nowadays.
Added: I have recently submitted a paper to the Monthly:
http://alpha.math.uga.edu/~pete/coveringnumbersv2.pdf
(By another coincidence, this paper is a mildly souped up answer to MO question #26.  But I did the "research" on this paper in the lonely pre-MO days of 2008.)
Looking at this paper helps me to see that the line between research and exposition can be blurry.  I think it is primarily an expository paper -- in that the emphasis is on the presentation of the results rather than the results themselves -- but I didn't have the guts to submit it anywhere without claiming some small research novelty: "The computation of the irredundant linear covering number appears to be new."  I'll let you know what happens to it.
(Added: it was accepted by the Monthly.)
 A: [Obsolete, see comments below.]
I have published a few expository pieces in The Australian Mathematical Society Gazette in recent years. 
A: The Journal of Commutative Algebra publishes expository/survey papers.  Your article on factorization might be appropriate, though I have not looked at it.  Disclosure: I am an editor for JCA.
A: Just in case, as it seems that nobody has already mentioned this above: Russian Mathematical Surveys (the English translation of Uspekhi Matematichekikh Nauk) also publish quite a number of high-quality survey papers which usually occupy most of the issue but these papers are almost always written by Russian authors (and, I guess, at least some of them are just solicited by the Editorial Board).
A: I'm not too familiar with Expositiones Mathematicae, but have you given them a look?
EDIT: The article I happened to have seen, which made me think that Expo Math might be along the lines Pete Clark was looking for, is this paper of T. Bühler - it modestly claims to no originality save for assembling disparate parts of the literature and writing down what's old news to connoisseurs (I'm paraphrasing here!) but of course this is, in a sense, precisely its originality & worth.
A: Dear Prof Clark,
I had a good experience a few years ago with Expositiones Mathematicae (an article on bump functions), and it seems that a fair number of colleagues happened upon it - so it is not obscure. This may be a good venue for you. I quite enjoy expository work, and lament the fact that many departments (and granting agencies) do not value them highly. Good Luck. 
R. Fry
A: The front page of the Notices (Jan 2011) is an advertisement for the "Bulletin of Mathematical Sciences". The "Aims and Scope" are:

The Bulletin of Mathematical Sciences, a peer-reviewed free access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (about 10 pages) containing significant results of wider interest. Most of the expository articles will be invited.

One of the executive editors is Efim Zelmanov, so that certainly counts as a "big-shot" getting behind the effort.
A: As it has not been cited before,  there is also a recent journal devoted exactly to what you suggest, Confluentes Mathematici (originally published by World Scientific, but now OA).
A: A new journal which could be better known and which publishes expository work is The Graduate Journal of Mathematics.
A: I too have thought that there should be such a journal, and found that Expositiones Mathematicae somehow doesn't stop me thinking that.
I think that if one were founding a new expository journal, then a very important feature that  it should have would be that getting an article into the journal should be prestigious. And for that it should be difficult to do. 
What makes it difficult to write an expository article? One obvious thing is if the mathematics you are writing about is very hard to understand. Sometimes, writing a good clear expository article involves digging deep into the thought processes of another mathematician who has not taken the trouble to say what they were, or of finding a clever way of presenting something that makes it much clearer where the ideas came from. Writing an expository article of this kind is pretty similar to research, in that it involves solving difficult problems. And one could argue that the value to other mathematicians of a good expository article is usually greater than the value of a good research article. (Perhaps I ought to change that "usually" to "often".) 
Other features of a journal that I think would make good sense are that it should be online and open access (with plenty of links to other internet resources such as blogs and wikis), and that writing about one's own work should be forbidden. Also, referees should not necessarily be experts in the area being written about, and should be encouraged to be completely honest if there are parts of the article they do not understand.
The advantage of an online journal is that with no pressure to produce issues on a regular basis one could keep the standard of acceptance very high. Perhaps one could even make it so high that the appearance of a new article would be something of an event. But the main thing is that it should be a significant contribution to a CV, or else the motivation for writing such an article would not be high enough.
A: And here is another journal that publishes long papers of "utility for a broad readership of specialists in the domain": Dissertationes Mathematicae. Apparently they quite often publish entire Ph.D. theses.
A: These journals say that they publish expository and/or survey papers...
Bulletin of the London Mathematical Society
DOCUMENTA MATHEMATICA
Global Journal of Pure and Applied Mathematics
International Journal of Modern Mathematics
INTERNATIONAL MATHEMATICAL FORUM
Journal of Analysis and Applications
Journal of Interdisciplinary Mathematics
Lobachevskii Journal of Mathematics
Logic and Analysis
Journal of Mathematical Sciences:  Advances and Applications
Surveys in Mathematics and its Applications  
Another possibility: Lecture Notes in Mathematics (Springer) or similar.  But only for longer expository pieces: Lecture Notes has a minimum of 100 pages.
A: I want to second Deane's comment on the usefulness of blogs (wikis). We can TeX, meanwhile, anywhere, anyhow. There could be a very fruitful symbiosis between blog and journal. The blog symbiont is the garden where expositions grow, perhaps fertilized if not seeded by commenters. Each symbiont consists of two poles: medium vs. reader. The journal symbiont faces the problem that its reader can not always write in it (or the marginals get closed away in one library somewhere). So, blogs (wikis) can also serve the marginals, something the medieval libraries knew to value.
This might hint at a new internet gadget. Which reminds me of another gadget: The user-sorted printout shelves, to be set up in and moderated by the library.
...Ooh, could amount to an extremely worthwhile internets programming project, including organizing real paper work, sort, and storage.
A: I am quite (quite, indeed) late on this one. A "good" journal which has probably gone unnoticed (didn't see any references in the answers provided) is the Milan Journal of Mathematics. Aims and scope:

Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists.

I remembered seeing an expository article of Heineken on complete groups published in its predecessor, Rendiconti del Seminario Matemàtico e Fisico di Milano. That is quite old though and I haven't recently perused Milan's contents to know if
it indeed does what it claims.
I guess Astérisque falls into category ii).
A: You could even try "Mathematics Student" published by the Indian Mathematical Society or "RMS Newsletter" published by Ramanujan Mathematics Society. 
A: On placing the expository paper  "Transseries for Beginners"
(too long for a comment)
Transseries arise when we complete things in a certain way by
including formal series, exponentials, and logarithms.  But they
have come up in non-trivial ways in many parts of mathematics:
real analysis, model theory, computer algebra, dynamical systems,
surreal numbers.  So it seemed that an exposition NOT using the
special knowledge or jargon of one area but accessible to all
would be good.  That is what this paper tries to be.
I tried at first to place it in a general-mathematics journal.
Starting with the Monthly.  But did not succeed.  So in fact
it will appear in the Real Analysis Exchange.  (One of the three
types of papers they publish are "survey" papers.)  And interested
people in other areas (who don't regularly scan the contents of
that journal) will have to find out about it somehow.
For the Monthly: The paper was 30 pages then, but still on
the borderline of being too long and on the borderline of being
too technical.  Journals I tried averaged 8 months to reach a
decision.  In all, from first submission (August 1, 2007) to
acceptance (January 31, 2010) was exactly two and a half years.
A: From their website:
"Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles."
A search in Math Reviews shows many articles in RMJM described as expository, either by the authors or by the reviewer.  Often there is disagreement as to whether a paper is expository, which indicates the utility of having  a journal that publishes both research and expository articles.
I am on the board of the Rocky Mountain Mathematics Consortium.
I have found it nearly impossible to write an expository paper that stays that expository.  New results have a way of being found by authors who are trying to clean up proofs of existing results.
A: The Electronic Journal of Combinatorics have these "Dynamic Surveys" which are allowed to be updated -- some of which are quite massive.
EDIT: It has been pointed out to me that there is another category, called "articles", in the Electronic Journal of Combinatorics which include non-dynamic surveys and exposition papers.  At the moment, there are not many such articles, but there are some (I counted 14 in total).

Research articles as well as surveys and articles of more general interest are welcome.

A: The AMS Bulletin publishes very high quality expository papers.
A: L'enseignement mathématique: http://www.unige.ch/math/EnsMath/
For longer papers: Ensaios Matemáticos.
Disclaimer/shameless plug: I was an editor of the latter.
A: It may seem to you like the market for expository papers has narrowed, but I think it has increased tenfold.  Personal blogs appear to be the medium of choice for exposition these days.  I am sure you are aware of this (in part because many high-profile Mathoverflow users have popular blogs), but I just wanted to remind you that blogs can reach a wide and interested audience.  Perhaps not everything belongs in a journal.
EDIT (Douglas S. Stones):  Adding to the "alternative to journals" answer -- authors could consider writing a book instead.
A: For probability theory, in addition to probability surveys already mentioned, the Séminaire de Probabilités (around one volume per year in the Lecture Notes on Mathematics, Springer) also publishes surveys.
A: SIAM Review (applied math, not pure math)
SIAM Review (SIREV) consists of the following five sections, all containing articles of broad interest:

*

*Survey and Review features papers with a deliberately integrative and up-to-date perspective on a major topic in applied or computational mathematics or scientific computing.

...
A: In probability, there's Probability Surveys. From their web site:

Probability Surveys publishes survey articles in theoretical and applied probability. The style of articles may range from reviews of recent research to graduate textbook exposition. Articles may be broad or narrow in scope. The essential requirements are a well specified topic and target audience, together with clear exposition.

A: There is a new journal of the European Mathematical Society that seems perfect for these articles: EMS Surveys in Mathematical Sciences. The description at the link reads:

The EMS Surveys in Mathematical Sciences is dedicated to publishing authoritative surveys and high-level expositions in all areas of mathematical sciences. It is a peer-reviewed periodical which communicates advances of mathematical knowledge to give rise to greater progress and cross-fertilization of ideas. Surveys should be written in a style accessible to a broad audience, and might include ideas on conceivable applications or conceptual problems posed by the contents of the survey.

I am actually quite excited about this, as there are some notes I've been sitting on trying to find an appropriate place for them. This may be the solution.
A: In fact, many journals give this option, but very few people use it.  For example, Discrete Mathematics has something they call "perspectives paper" which is basically high quality survey paper on a novel topic or a novel technique:  http://tinyurl.com/yh9swnn  My understanding is that these perspectives paper undergo the usual refereeing process. 
P.S.  Full disclosure - I am an editor of DM.
A: This used to be a post about the
Central European Journal of Mathematics which has changed quite a bit since the writing of the original post.
I no longer endorse that journal.
The true successor of the original spirit is the European Journal of Mathematics, whose Editorial Board is essentially what used to be the CEJM editorial board which resigned in its entirety as a group in protest of the publisher's actions with regard to the journal.
Here is some more explanation in response to the comments:
Keith and Darij:
Perhaps calling the journal evil was too much, I meant that for the publisher.
Here is what happened. De Gruyter acquired the journal a few years ago and immediately decided to change its philosophy. They call it "open access", which means that you can access the published articles free of charge, but in order to publish an article you have to pay €1000 (see https://www.degruyter.com/view/supplement/s23915455_Article_Processing_Charges.pdf). At the time of enacting this policy they even decided to charge those authors whose paper had already been accepted, but had not yet appeared in print. The Editorial Board protested this action, but De Gruyter ignored us. In addition, it seemed that the emphasis was on charging the authors not on the quality of the publication. I cannot speak for the current Editorial Board, but back then we felt that the publisher's model would potentially lead to a journal where people can simply pay to get published which would naturally lower the quality of the publication. The fact that the publisher decided to charge those whose articles had been accepted within the free-to-publish model was a bad sign and did not reflect well for the resolution of potential future issues. I do not claim anything about the current state of the journal, I simply wanted to withdraw my endorsement.
A: Apparently the Japanese Journal of Mathematics is focused on survey/exposition papers:

The official journal of the Mathematical Society of Japan, the Japanese Journal of Mathematics is devoted to authoritative research survey articles that will promote future progress in mathematics. It encourages advanced and clear expositions, giving new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years.

A: You can certainly find such journals if you are not too career-minded. Although there are not many examples in recent issues, Rendiconti Torino
has open access and a tradition of publishing occasional expository articles, though typically less than 30 pages. It will effectively referee such papers provided that they appear to have a novel approach (as is the case of yours) thta cannot be found elsewhere. Publishing in such a journal may be more satisfying than simply leaving a paper on a homepage or the arXiv (which you can still do anyway). [I am its director, but it's a non-profit concern and I feel that such publicity is in the community's interest.]
A: The Moscow Journal of Math says they publish "research-expository articles."  
"An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists."
I'm not sure exactly how that plays out in practice, I haven't submitted any articles there.  But it looks like it's worth a try for certain sorts of articles with significant expository content.
A: I just wanted to comment on Pete's answer to Felipe Voloch but it seems I can't so I'll write an answer instead. I think that L'Enseignement Mathématique does publish purely expository papers. I have two examples in mind (hope I'm not mistaken):


*

*L. Illusie "Catégories dérivées et dualité: travaux de J.-L. Verdier" Enseign. Math. (2)  36  (1990),  no. 3-4, 369--391

*J. Nicaise "Formal and rigid geometry: an intuitive introduction and some applications."  Enseign. Math. (2)  54  (2008),  no. 3-4, 213--249

A: There's an online Mexican journal Morfismos that seems to specialize mainly in surveys.
It seems to be a small-ish operation, but they've published expository papers by well-known authors such as Snaith, Landweber, Kontsevich, and Kervaire. Unfortunately they are not listed on Math Reviews yet, but I understand this may be in their future.
A: I just came across the following new publication. SpringerBriefs in Mathematics. (Somewhere between a paper and a book; 50-125.)
I think It is not what was originally asked for, but might be close to some things that came up in the discussion.
Since it is new, and I only know what is written on the webpage, the relevance of this to the subject at hand is not yet completely clear to me. Still, I hope it is close enough to be on-topic. [Some of the text below is the same for all Briefs in different fields, which might explain some possibly surprising formulations.]
From https://www.springer.com/series/10030
Excerpts from the page.
SpringerBriefs present concise summaries of cutting-edge research and practical applications across a wide spectrum of fields. Featuring compact volumes of 50 to 125 pages, the series covers a range of content from professional to academic.  [...]
Typical topics might include:
.) A timely report of state-of-the art techniques
.) A bridge between new research results, as published in journal articles, and a contextual literature review
.) A snapshot of a hot or emerging topic
.) An in-depth case study
.) A presentation of core concepts that students must understand in order to make independent contributions
SpringerBriefs in Mathematics showcase expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians, applied mathematicians.
A: Just last night I was looking for a journal that would accept a (largely) survey paper with some new results. I discovered for myself Aequationes Mathematicae. I had previously considered Expositiones Mathematicae, but had uneasy feelings about it since it is Elsavier (my first and only, and very recent, experience with Elsevier was not a pleasant one). Aequat. Math. is published by Springer (however, see my comments below about Springer).
From the description of Aequat. Math.:

$\bullet$ An international journal of
pure and applied mathematics, which
emphasizes functional equations,
dynamical systems, iteration theory,
combinatorics, and geometry.
$\bullet$ Publishes research papers,
high quality survey articles, reports
of meetings, bibliographies, and
summaries of recent developments and
research in the field.
aequationes mathematicae is an international journal of pure and
applied mathematics, which emphasizes
functional equations, dynamical
systems, iteration theory,
combinatorics, and geometry. The
journal publishes research papers,
reports of meetings, and
bibliographies. High quality survey
articles are an especially welcome
feature. In addition, summaries of
recent developments and research in
the field are published rapidly.

However, it seems that they rather restrict the spectrum of fields in which they publish (the first point above).
A few words about Springer: Depending on your view on science journals, you may have uneasy feelings about publishing in Springer. It seems that some mathematicians are considering boycotting Springer (e.g. J. Baez here) for various reasons (such as rising journal costs). I don't know much about this issue, but we all know about the situation with Elsevier.
A: Have you considered writing a Math blog ? Or sending your original paper for 'invited post' to an existing math-blog writer with appropriate scope and audience. Math blogs don't have the permanence of a math journal. But I'm pretty sure they get more attention from students than Expository math journals.
Your question reminds me of one of my favorite math paper Fractions by L.R. Ford in Amer. Math. Monthly Vol. 45, No. 9 (Nov., 1938), pp. 586-601. The first sentence of the paper is particularly delightful when thinking of the far reaching consequences this paper had. Take Rademacher exact formula for the partition number for example...
