Hmm, you haven't given us much to go on, so if you don't have a gaming PC:
Gears of War - Third Person Shooter
Call of Duty 4 (better than 5 imo, singleplayer is short but good, and the multiplayer is decent fun for a while) - FPS
Battlefield Bad Company - FPS
Eternal Sonata - RPG
Mass Effect - RPG/Shooter
Project Gotham 4 - Driving
Banjo-Kazooie: Nuts and Bolts - Platformer /w Driver elements
Resident Evil 5 - Coop Survival Horror
Dead Space - Survival Horror
Crackdown - Freeroaming Crimefighting, minor RPG elements
Burnout 3 - Driving
Fable 2 - RPG
Oblivion GOTY Edition if you haven't played it already, marmite game though - RPG
Streetfighter 4 - Fighter
Fallout3 - RPG/Shooter
ALSO - checkout:
http://www.metacritic.com/games/xbox360/scores/
Its USA based (so some games may not be out yet here), but has a collected review system; if its high up the scoreboard, it got a very high overall score from multiple reviews. Should help you find some good games
There are some great games out!