All the ones mentioned above are great. I'd like to throw out specifically additional recommendations for The Orange Box(action/adeventure), Call of Duty 4(FPS/war) and Mass Effect(RPG) though.
Crackdown is a great, fun game to just pick up and play for no reason.
Are you adverse to Xbox LIve Arcade games? If not there are TONS of great ones. Undertow is popular. I liked it alright, but people seem to love it. Puzzle Quest is a GREAT puzzle/RPG game. There are several good card games for casual downtime, such as Uno, Hardwood Spades and Texas Hold'em. There are great puzzle games, Lumines Live! (a favorite of mine), Zuma (TotalMILFs favorite) and Geon. Classic video games like Contra, Ms. Pac Man (also Pac Man CE which is awesome) and Castlevania.
Seriously? There are so damned many good 360 games I have no clue why anyone would by any other system
Rock Band is good, but if you don't have the $$$ for it, Guitar Hero III is pretty good as well (though I prefer Rock Band). Scene It! is good for casual parties (like, of the drunken but not crazy variety) or for just lounging with the SO, family or friends.
Timeshift is pretty good. Not GREAT, but unique enough to be interesting. As is Army of Two if you have someone you can co-op with.
Hope that helps!