I don't own a 360, but if I did, I can say that I would most definitely buy a ton of JRPGs for it, so long as I could find them.
On a general basis (all consoles), my favorite genre of games consists of something like this: RPG (JRPG, animal guardian sim [Digimon / Monster Rancher / Dragon Quest Monsters], fighting RPGs like Tales of, Final Fantasy, ARPGs like Kingdom Hearts and The World Ends With You, Megaman Battle Network & Starforce), Action-Platformer (Sonic, Megaman [classic, zero, some X]), Racing, and music like bemanistyle games (DDR, beatmania, pop'n music) (can't stand guitar hero or rock band).
Oh, and I love the SSX games, though boarding (air, snow, water, skate) games are about as far as I go in sports. (no basketball/football/soccer) ...Wii sports resort's fencing was fun though.