Survival Horror, fighting, Shmups, music, RTS.
Take fighting as a random example.
In the PS2 generation, there were several Street Fighter games, Marvel vs Capcom 2, several Guilty Gear games, some SNK stuff, Melty Blood, a few Tekkens, a few VF games, a few Dead or Alive games, two Soul Calibur games, and a bunch of Mortal Kombat. I'll also include Smash Bros just to sidestep that debate. I'm sure I'm missing a few things (Arcana Heart comes to mind), but just let's call this a representative sample.
Street Fighter -> Still around, 4 considered a renaissance of sorts by many
MvC -> still around, more prominent than ever
Guilty Gear -> Did exist for a while, decline, ASW now working on BlazBlue
SNK -> Less of a player but still around.
Melty Blood -> I'm pretty sure they're still releasing these.
Tekken -> 123 = PS1, 45 = PS2, 6 = current gen. TTT1 = PS2, TTT2 = current gen. If you count the PSP spinoff/port/whatever of 5 as last gen, and count the 3DS one as this gen, that's equal. Plus SFxT and TxSF.
VF -> Fewer installments, but VF5 is current gen
Dead or Alive -> Still exists current gen
Soul Calibur -> Still exists current gen
Mortal Kombat -> Fewer SKUs this gen, but MK2011 generally well received.
Smash Bros -> 1 last gen, 1 this gen.
Besides BlazBlue, Skullgirls will be a new fighting IP this generation. There's a lot of quantity, and many of these games have been pretty high quality. I'm not a fighting fan, so maybe you liked some of the older stuff better than the newer stuff, but in terms of quantity and reception, seems pretty on par. I guess Capcom is doing less low-tier stuff (no more Rival Schools, Darkstalkers, JoJo, etc) but I don't think you can conclusively say that that means fighting has dropped off as a genre.
And then there's the elephant in the room. Most fighting games are online now. Which is kind of a big deal.