[b/]Bioshock[/b]-One of the most immersive games I've ever play.
[b/]Mass Effect[/b]-Really great RPG
[b/]Left 4 Dead[/b]-A really intense gaming experience which will make you swear like a f*%$er
[b/]Call of Duty 4[/b]-Really great game single player game with a decent multiplayer conponent
[b/]The Orange Box[/b]-Best deal in gaming ever, 5 big title games in one box for the price of one. Much better on the PC it has to be said but still deffintly worth a look. Even if you don't get it, for whatever crazy reason, buy [b/]Portal[/b] on the xbox live arcade, as its a piece of genius.
You may also want to check out a few xbox origanals on the marketplace or from a bargain bin, buy [b/]Psyconauts[/b] and [b/]Prince of Persia: SoT[/b] if you can get your hands on them.
There also some great aracade titles. I've already mentioned Portal, but theres also [b/]Castle Crashers[/b], a multiplayer aracade game with a very cartoony look and flatulant woodlend creatures. OH and my god, please do get [b/]Braid![/b] Much like Portal, its a work of genius.