Right now I play almost exclusively on 360 because my PC is ancient and the Wii has few fun games.
Online, I love Super Street Fighter IV! Tekken 6 is also really good but I don't play it nearly as often. As far as shooters, I don't stick really hard on any one, but MW2 is fun and R6Vegas2 is awesome. Gears of War online is good but I haven't played in a long time... I'll probably jump back in when 3 releases.
Offline, my favourites are RPGs, music/rhythm games, and hack & slash in the vein of BG:Dark Alliance or Champions of Norrath.