A lot of the games on here I agree with. So I'll just mention ones I haven't seen on my quick scan through:
- Assassin's Creed- the original. I saw 2 recommended, but I'd definitely say that you should play the first one... well... first.
- Tales of Vesperia- as long as you don't mind the anime aesthetic (which I'm guessing you don't, from the avatar), this is a great game.
- Devil May Cry 4- yes, it wasn't quite as good as DMC3, and there was a fair bit of repetition, but I found it fun enough to justify a purchase.
And, that being said... I second Bioshock, the other Assassin's Creeds, Fable II, Infinite Undiscovery, The Orange Box, and the Bioware games.
(...And, really, random poster? I never knew being female meant that I should own a Kinect and a dancing game. ...I'm such a failure. /sarcasm)