I've had different favorite genres for each generation.

PS1/N64 Gen - Platformers

PS2/GC - RPG

PS3/Wii - Action/Adventure

JRPG, SRPG. Though I feel the latter is pretty much a sub-genre of the first, so I'd throw in Adventure as well.

Given the relative lack of relevant games on the home consoles in the beginning of this gen, I attempted to get into other genres as well, without much success.

First Person everythings, which then has to go to Shooters first and platformers/stealth/action-RPG second (not soo much RPGs see Bethesda's - i think it's about pacing), but that is more true for PC than consoles, because of the controll system. The reason is immersion.

Still the main representative of those games this gen is Mirror's Edge (played on PS3). Not the PS3 FPSs because of the controll issue.

On consoles though there is another genre that I enjoy which is much more suited to be controlled with a pad  console controller, Action/hackand slash:

Heavenly Sword, DMC4, Darksiders (and last gen's played on this gen hardware, DMC3, GoW1 and 2).

Computers

Turn Based Strategy, Simulation (only because of the sims and sim farm) and RTS

Consoles

360 - Shooters, Turn Based (civ rev), Fable type games

PS3 - Platformers

Sega Mega Drive II (seriously was there a first, I never saw it)... EVERYTHING!!! I played the death out of Super Monaco GP and After Burner, I even played the recent on the 360... that game is awesome, no other pilot games/ racing games got me like those 2. Zombies! ate my neighbours was lots of fun too.

1st. Platrofms

It's too difficult for the others, I like action/shooters, Adventure games, RPGs, Fighting games and Driving Games but I can't make an make a rank.

I generally don't like sports games, hack and slash games.

There are three genres I personally I can't get into - Hack and Slash, Fighting Games and Sport games, although I do play like 1 or 2 games of FIFA 2004 <- The only Fifa I have. The only Hack and Slash game that I sort of liked to an extent was Ninja Gaiden 2, but that was "Oh my god fml" hard for me, so I didn't get very far. Fighting games I've only really played SSFIV and DC vs Marvel, couldn't really get into them.

I am a fan of FPS genre since Half Life/Counter Strike mod, but I think what really defined it for me was COD4!