Quantitatively speaking, which subject area in mathematics is currently the most research active? I was wondering if there is a list of the most active branches of mathematics?
If MathOverflow is a representative sample, then algebraic geometry is by far the most popular.  Is this the case?
 A: The word "current" is my get-out on this!  Here's the data from the arXiv for the month of december:
118 math-ph
111 math.PR
111 math.DG
 97 math.AG
 96 math.NT
 91 math.CO
 87 math.AP
 71 math.DS
 45 math.GR
 43 math.RT
 35 math.FA
 32 math.GT
 31 math.OC
 30 math.ST
 30 math.QA
 30 math.CA
 28 math.AT
 26 math.CV
 25 math.AC
 24 math.RA
 23 math.SG
 22 math.NA
 19 math.OA
 17 math.LO
 16 math.MG
 12 math.GM
 11 math.HO
 11 math.CT
 10 math.KT
  8 math.GN
  6 math.SP

(yeah, yeah, I know - skewed results since it came from the arXiv ... yawn, think of a new complaint, please.)
A: "Fashionable" is so subjective that it should be avoided here, I think.
On the other hand, it is very natural to wonder about which subject areas -- as represented, say, in the 2010 AMS Mathematics Subject Classification -- are the most popular as measured e.g. in terms of total papers published in the last ten years or the total number of mathematicians who have published in this area.  
I'm not about to try to implement a computer search to answer this question, but it seems likely that someone else has already done so.  I will predict an answer though: algebraic geometry is not the most popular research area in any quantitative sense.  (Others have asked why algebraic geometry is so prevalent on MO and the most convincing answer seems to be that the founders of MO are mostly algebraic geometers and mathematicians in closely related areas.)  I would be willing to bet that, as has been the case for at least one hundred years, more papers are published in analysis than in any other area.
A: I think it is a little bit anachronistic to divide mathematical disciplines
and search for the most "active" one. The modern tendency (justified by
the major achievements of contemporary mathematics) is to ignore the
"barriers" between the different fields and become truly interdisciplinary.
A: I'm skeptical that this question can be asked and answered in a meaningful manner. Do we really want to know which area of mathematics produces, say, the most papers? Or even the most citations? What might be more meaningful (but maybe not) is which fields get the most funding from NSF.
A: For those who have time to do some coding, the AMS releases tables of how many papers in MathSciNet land in each of the MSC subjects.  This should be a more representative sampling of mathematical publications than the arXiv. Unfortunately, the format is a list of every paper, its year of publication, and which classifications it used, so it is not obvious to a human which subjects are the most popular.
For those who don't have the energy to create our own table, David Rusin has a chart where the area of each MSC subject is proportional to the number of publications in that filed from 1980-2000. The classification is too fine to easily answer questions like "Is analysis more popular than algebra" and the time period is not quite what we want. But one can immediately see that any one of Statistics (62), Probability and Stochastic Processes (60), Numerical Analysis (65) and PDEs (35) all dwarf Algebraic Geometry (14), Category Theory (18) and even Number Theory (11).
