I personally enjoy platformers the most (Super Mario World, Sonic the Hedgehog, Crash Bandicoot) only because I grew up with them. Just recently, I have entered into the world of Adventure games (Zelda) and shooting games (Halo).

Fighting, Stealth Action, RPG.

Anything but RTS (and yes, that even includes text-based adventure games like the original Zork) - never could get into them that much, but I've tried...

Edit: Actually, I liked RPGs before, until I played Final Fantasy XI (or whatever number it was) - the rote turn-based combat system killed the gameplay for me. 

Sports, and ... the "misc." type.   No FPS, RTS, FPS, fighting, action, adventure, or basically anything that falls under a category.

"misc.":  you know, like DDR, brain training, phoenix wright. 

 i used to like turn based strategy, like civ, and the RTK's.  but now i'm impatient and they just consume too much time.

i also used to like turn based RPG, though very selective.  but again i've grown impatient and they just take way too much time and effort.

the type with std infested prostitutes. those are my favorite

1. RPG (only if the story is interesting enough to keep me playing) 2. Platform (I probably actually like more games in my number 2 but the RPGs that i enjoy blow all platformers away) 3.Most anything Fighting, Racing, Simulators, Adventure, RTS, Party pretty much just not sports games or Massive Online games

Platformers, because I grew up with them and playing New Super Mario Bros showed me that I still prefer that genre. But in the meantime, RPG's came very close and I really love them too now.

strategy games. Homeworld/Advance wars/Starcraft are the greatest RPG's. but only the ones where you get a say in how your character progresses (ie, Baldurs Gate and Diablo 2, not Final Fantasy/Dragon Quest). The fun is building your character, what's the point if you don't get any choice?