Top specialized journals In geometry/topology, there are (at least) three specialized journals that end up publishing a large fraction of the best papers in the subject -- Geometry and Topology, JDG, and GAFA.
What journals play a similar role in other subjects?  
Let me be more specific.  Suppose that I'm an analyst (or a representation theorist, or a number theorist, etc.) and I've written a paper that I judge as being not quite good enough for a top journal like the Annals or Inventiones or Duke, but still very good.  If I want to be ambitious, where would I submit it?
Since the answer will depend on the subject, I marked this "community wiki".
 A: I think the following journals are the top 3 journals in numerical analysis:


*

*Numerische Mathematik

*SIAM Journal on Numerical Analysis

*Mathematics of Computation
A: For algebraic geometry, I would think that Journal of Algebraic Geometry is the top specialized journal. However, there are many excellent journals that are nominally in a different (neighboring) field, which accept algebraic geometry submissions (and have algebraic geometers, or people interested in algebraic geometry, in the editorial board). Examples include:


*

*JDG

*Geom. & Topol.

*Algebra & Number Theory

*J Topology.


(Of course, there are also many other non-specialized journals that are suitable for an article that is almost Inventiones- or Duke-level.)
A: Disclaimer: I am a founding editor of one of the journals listed here.
In the field of computational geometry, there are four specialized journals, that I would rank in this order:

*

*Discrete & Computational Geometry (DCG) - Wikipedia

*Journal of Computational Geometry (JoCG) - Wikipedia

*Computational Geometry: Theory and Applications (CGTA) - Wikipedia

*International Journal of Computational Geometry and Applications (IJCGA) - Wikipedia
I don't think anyone who works in the field would dispute the relative rankings of DCG, CGTA, and IJCGA.
JoCG is another story. It's a relatively new open-access journal, established in 2009. I place it second here because I think that's a fair estimate of how good a paper has to be in order to get accepted in JoCG. If you measure quality in other ways, you may rate it differently.
A: Disclaimer: I am not an algebraist, although I've played one on occasion, hence I've decided to get the ball rolling for Algebra journals.
I have heard that Journal of Algebra publishes some good papers, but that the quality can vary a lot.
Any other algebraic journals out there that people recommend?
A: In PDE and related analysis, there are a lot of good journal, among which the recent Analysis and PDE (by MSP, the publishers of Geometry & Topology) and the much older Archive for Rational mechanics and Analysis seem to stand on top. Also noticeable are Annales de l'IHP - analyse non linéaire, Communication on PDE, SIAM journal on mathematical analysis, and certainly other that I forget.
A: In the field of statistics, there used to be three journals that are tops:


*

*Journal of the Royal Statistical Society: Series B 

*The Annals of Mathematical Statistics. (Changed its name to
"Annals of Statistics" since 1970s, each issue is like a history since you can see many different names with a couple of methods named after them.)

*Biometrika (due to the influence of Fisher-Pearson school)


Now there are "new three" with an emphasize in new-era machine learning interest:


*

*Journal of the American Statistical Association (due to the fact that many machine learning literatures are published on it, which is a good example of the drift of the trends in a branch of mathematics.)

*Annals of Statistics. 

*Journal of the Royal Statistical Society: Series B 

A: The following is my personal (i.e., includes all of my mathematical prejudices) ranked list of subject area journals in number theory.
From best to worst:
1) Algebra and Number Theory
2) International Journal of Number Theory
3) Journal de Theorie des Nombres de Bordeaux
4) Journal of Number Theory
5) Acta Arithmetica
6) Integers: The Journal of Combinatorial Number Theory
7) Journal of Integer Sequences
8) JP Journal of Algebra and Number Theory
For a slightly longer list, see 
http://www.numbertheory.org/ntw/N6.html
but I don't have any personal experience with the journals listed there but not above.  
Moreover, I think 1) is clearly the best (a very good journal), then 2)-5) are of roughly similar quality (all quite solid), then 6) and 7) have some nice papers and also some papers which I find not so interesting, novel and/or correct; I have not seen an interesting paper published in 8).  
But I don't think that even 1) is as prestigious as the top subject journals in certain other areas, e.g. JDG or GAFA.  There are some other excellent journals which, although not subject area journals, seem to be rather partial to number theory, e.g. Crelle, Math. Annalen, Compositio Math.  
Finally, as far as analytic and combinatorial number theory goes, I think 4) and 5) should be reversed.  (Were I an analytic number theorist, this would have caused me to rank 5) higher than 4) overall.)  
A: (This would have been a comment but I do not have that privilege.)
I just want to ask if there's a significant difference in reputation between the Journal of Combinatorial Theory (JCT) series A and series B?
As far as I was aware the split is purely on subject area, e.g. enumerative combinatorics in A and graphs and matroids in B.
Scanning through the answers I saw JCT:A mentioned a couple of times but did not spot JCT:B being mentioned. Is there a feeling A is of a higher level?

Since I had to make this an answer, let me give, the obvious, answer for discrete geometry. The best subject specific journal in that area is Discrete and Computational Geometry.
A: Combinatorics:  In my opinion, Discrete Mathematics is only a mediocre journal (I wouldn't consider this top journal).  Yes, it contains good papers, but it contains a lot of papers... on average... it's average.
Some other ones worth a mention (on top of JCTA, JACO and EJoC mentioned earlier): Journal of Combinatorial Theory Series B, Journal of Combinatorial Designs, Annals of Combinatorics, Combinatorica.
The Electronic Journal of Combinatorics should probably go on the top list in combinatorics, but since it's a free, open access journal, it's usually assumed to be worse than it actually is.

Combinatorics, Probability, and Computing, the Journal of Graph Theory and the Electronic Journal of Combinatorics seem to be widely regarded as excellent journals, at the level of the ones mentioned above (except Discrete Mathematics).
Formerly, the "Journal of Combinatorics" referred to a printed version of the "Electronic Journal of Combinatorics" (which has led to some confusion, see e.g. https://symomega.wordpress.com/2010/03/30/the-arc-the-era-and-the-ejc/), although most people in combinatorics haven't even heard of it.
Joel Reyes Noche's comment points out that there is a new journal entitled "Journal of Combinatorics".
A: In mathematical physics, Communications in Mathematical Physics is among the top journals I guess.
There are two other journals I would consider to be above average: Advances in Theoretical and Mathematical Physics and the Journal of High Energy Physics, which publish lots of high-quality mathematical physics papers, especially at the formal end of hep-th.  Of course, I have heard if mentioned in the past that, especially in US maths departments where they care about this sort of things, Communications is considered a mathematics journal, whereas JHEP perhaps is not, the jury still being out on ATMP.  Hence if you are a mathematician thinking of publishing a good paper in mathematical physics and want to publish in what potential employers might consider (however narrow-minded this consideration might be) a mathematics journal, then perhaps Communications is the way to go.  The quality of papers there is consistently above average.
A: In probability, The Annals of Probability is certainly leading the field, probably along Probability Theory and Related Fields. 
In fact, the leadership of The Annals of Probability is so strong that many probabilists seem to not even think of top generalist journal when they have a top result, and simply submit to The Annals of Probability papers that would have a shot at Inventiones and the like. At least, it is what some papers there made me think.
As noted by Martin Hairer, there are several other probability journals that are high level, though less universally considered on top of the field: Electronic Journal of/Communications in Probability (which is remarkable by being free for the authors as well as open for readers) and Annales de l'IHP: Probabilités et statistiques.
A: In ergodic theory and dynamical systems the top specialized journal is... well, Ergodic Theory & Dynamical Systems. By a country mile. I don't think any other journal in this area deserves to be mentioned here. 
A: Combinatorics: JCTA (Journal of Combinatorial Theory: Series A) and JACO (Journal of Algebraic Combinatorics)
Enumerative combinatorics: Discrete Mathematics journal (DM), European Journal of Combinatorics.
A: My view for Combinatorics :
1.The Electronic Journal of Combinatorics
2. JCTA and JCTB
3. European Journal of Combinatorics
4. Combinatorics, Probability, and Computing
5. Journal of Alg. combinatorics
6. Journal of Graph Theory
7. Combinatorica
8. Integers
9. Discrete math
A: This is a list of top journals in Mathematical Logic ranked according to my personal point of view:
1- Journal of Mathematical Logic
2- The Journal of Symbolic Logic
3- Annals of Pure and Applied Logic
4- Fundamenta Mathematicae
5- Notre Dame Journal of Formal Logic
6- Archive for Mathematical Logic
7- Mathematical Logic Quarterly
There are other journals which I'm not able to locate in the list above. Among them is the prestigious "The Bulletin of Symbolic Logic":

*

*The Bulletin of Symbolic Logic


*Studia Logica


*Logic and Algebra


*Logical Journal of IGPL
Also, we have the journal "Model Theory" which has started publishing since the beginning of 2022.
