Action
Gears of War (First one, second will probably be late '08 or '09)
Halo 3 (Great fun with 1-3 other people on single player legendary)
Army of Two (Didn't like it single player though, online coop should be fun)
Mass Effect (Action RPG, at least 40 hours of gameplay on your first play through, took me 55)
Assassins Creed
Condemned: Criminal Origins (Top 5 360 title for me, bloody excellent)
Crackdown
N3
Lost Planet: Extreme Condition
LEGO Star Wars: The Complete Saga (Awesomely fun)
FPS
Call of Duty 4
Call of Juarez
F.E.A.R
Prey
Bioshock
Orange Box
Racing Sim
Forza 2
Test Drive Unlimited (Never played it myself, it's an online open world thing)
Racing Arcade
Burnout Paradise (Crash into things at high speed...a lot)
Colin Mcrae - DiRT
Sega Rally (Uber Arcade, don't expect anything realistic from this)
Definitely pickup Oblivion if you haven't already played it, great (albeit a bit too shallow for the hardcore wizards) RPG.
Also go to
http://www.lovefilm.com/freegift and put the code XMLFZZ711 and click 'rent games as well' somewhere along the line (where you choose your package), and choose combination 3 DVDs & Games. You'll get 3 months of free game rental, can get loads of titles in the time. MSN is in trust if you need any help setting it up.