God, I dunno. A lot. Generally on PC these days, few exceptions. Steam library is just shy of 200 titles, though that may not be a lot compared to some of you avid geeks.
Generally my favorite genre is well done FPS/RPGs and oldschool PC WRPGs. I like TBS and RTT games (Wargame: EE, Company of Heroes, Myth 1 & 2, Civ / 4X strategies), but I just get lost in action-per-minute = success RTS like starcraft.
Alltime favorite titles are Bioshock / System Shock, Fallout 1 2 Tactics 3 NV, Deus Ex 1 HR, Halflife, Tribes 1 2 Ascend, Battlefield(s) 1942 - 3, Doom / Quake 1 2, Elderscrolls 3 - 5, Grand Theft Auto (all ex: mobile games), Company of Heroes, Dawn of War 1 - Dark Crusade, Minecraft, Dungeon Keeper 1 2, Halo 1 & Reach, etc etc...
I dunno, I'm pretty omnivorous. If you give me a game I'll give it a fair shot, but certain types do really turn my crank.