Having read a thread on a similar question on expository papers I'm reminded of reason #99 to drop my math PhD thingy, late c20th: I just couldn't blow up this paper to 4 pages. (OK, one halfpage calculation was left to the expert reader (and other experts could guess), but...)

1$\begingroup$ I believe many journals do, when appropriate. Off the top of my head, I remember seeing 1 page papers in the Journal of Symbolic Logic and in Transactions of the AMS, for example. $\endgroup$ – Andrés E. Caicedo Sep 23 '10 at 5:14

23$\begingroup$ If you find out, let Noam Elkies know. He has about a dozen onepage papers at math.harvard.edu/~elkies/Misc/#papers $\endgroup$ – Gerry Myerson Sep 23 '10 at 5:36

2$\begingroup$ Well, I'd guess that many journals do, provided the content is appropriately interesting, as Andres commented. I've heard that in Japan, for instance, "publishing culture" is very different  many one page papers with completely random results. Then again, this makes me wonder: where does one draw the line between rigor and unnecessary pedantry? Take Garry's link as an example. Or, better yet, Perelman's proof of Poincare's conjecture. As I understand it, people who filled in some parts of his proof felt that they had done enough to claim the result entirely. $\endgroup$ – user39719 Sep 23 '10 at 5:59

5$\begingroup$ Transactions of the AMS is a journal that has a lower bound on length; they would direct any 1 page paper to Proceedings of the AMS (which only publishes short papers). Comptes Rendus Mathematique only publishes short papers so would probably be a natural place to look. $\endgroup$ – Sheikraisinrollbank Sep 23 '10 at 10:58

$\begingroup$ "Comptes Rendues" usually publishes short versions of existing longer papers (or theses)  this is actually the meaning of its title. $\endgroup$ – anonymous Jul 8 '12 at 16:59

1$\begingroup$ Wow. Phantastic list. I'll print out almost all. That will give me stuff to read for the rest of my life... $\endgroup$ – Martin Gisser Sep 23 '10 at 6:39
The American Mathematical Monthly publishes several short "Notes" in each issue, and I'm sure I've seen several that were only about a page. As you would expect (being published by the MAA), many of these are mainly of pedagogical interest, but there are also some very interesting and nontrivial ones.
Generally, journals rarely seem to have an explicit lower bound on the lengths of the papers. If they do, they will explicitly tell you so, and in those cases, the same society often publishes a journal for shorter papers.
If you proved an important result in a readable way on one page, almost no decent journal would ask you to add a bit of waffle to fit their criteria. So the question you should be asking is "which journals publish results of fill in importance/generality or on the topic of fill in". Having said that, there are a few journals who particularly specialise on short papers, i.e. have an upper bound on length rather than a lower one. In addition to what has been suggested, you can have a look at the Bulletin of the LMS (the LMS also issues two other journals for longer papers). Also, the Bulletin of the Australian Mathematical Society promises short turnover times, which suggests that they like short papers. If you think that your paper is first class, then you can also consider the Annals of Mathematics, since they have a policy of encouraging short papers (by which they mean under 20 pages).
But as I say, I genuinly believe that no journal is going to turn down a paper because it is too short, unless this is their explicitly stated policy. So just choose a journal that you think is interested in your result.
On the other hand, unless you think that the brevity is a selling point of your paper, why don't you add a few examples to illustrate the interest or the usefulness of your result?
Here is an example of a 3 page paper in the Annals of Mathematics:
Hart Smith, An elementary proof of local solvability in two dimensions under condition $(\Psi )$, Annals Math, 136 (1992), 335337.
So this is another piece of evidence that most journals have no objection to shortness in papers, even below 4 pages. (This paper is not in my research area, but I know about it from knowing the author.)
Proceedings of the AMS likes short papers. Looking at their most recent table of contents, I see between 413, with the median probably around 9. I think they would be open to a 1 page paper.

4$\begingroup$ I once published a half page paper (including the references) in PAMS ... is this a world record? S. Thomas, Fixed points of automorphisms of finitely generated free groups, Proc. Amer. Math. Soc. 103 (1988), 333. $\endgroup$ – Simon Thomas Sep 23 '10 at 11:51

4$\begingroup$ no, not a record. See the thread mathoverflow.net/questions/7330/… for a few more, including one which was 6 lines long. $\endgroup$ – Gerald Edgar Sep 23 '10 at 14:20
A lower bound on paper length would make little sense  if something can be proved very quickly, but the proof is novel and the result is interesting enough to justify the publishing process, then so much the better. (With very important results, sometimes you'll even see papers in wellregarded journals entitled 'A Short Proof of (already known result)', because short, clear proofs are valuable even when other proofs are known.) One note of caution though: if you are a 'hobby mathematician' as you say in your profile, and you have an unusual writing style, you may have to work extra hard to overcome the referee's scepticism. This is a reason to write more detail rather than less, especially in the initial submission. You can always trim it down later if that's what the journal wants.

$\begingroup$ The 'hobby mathematician' refers to what I'm pursuing now, c21st: Not serious fulltime research on new things, but digesting old stuff my way, when I got spare time and inspiration. I might return to doing a math PhD when I'm 70, ca. 2040  if planet and civilization haven't burned down then. But I will revisit/rewrite my late c20th paper and try to seriously publish it, if the result isn't meanwhile known. $\endgroup$ – Martin Gisser Sep 23 '10 at 16:33
I just stumbled across a very recent example (2017) at the Archiv der Mathematik which I felt compelled to add to this list.