"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.