Platformers
Love retro platformers, as well as some Mario platformers (64, Sunshine).
Shooters (Online or offline)
Valve games, Metal Gear Solid series
Music Simulators
Guitar Hero/Rock Band, fun some times.
Strategies
Can't remember which one(s) I liked in this area.
Real-time Strategies
Can't remember which one(s) I liked in this area.
Adventure/Exploring Games
Action/Adventure would include Zelda, I'd assume
Sports Games
Only the Mario ones, like Golf and Tennis.
Racing Games
Mario Kart.
Simulation Games
The Sims 2/3 is fun from time to time.
Stealth Games
Metal Gear Solid series, again.
Whatever Ace Attorney would be under, that game genre as well.