I'm late to the party but I just got my Xbox 360 last week. I won it in a charity raffle for $50, and it took them this long to get it to me. Ah well, can't beat the price!
I just have to say that Geometry Wars is a pretty kickass game. For about $5 you get the game off Live Arcade. It's like a classic asteroids type shooter but hyped up on steroids. Definitely worth $5.
Otherwise, I know there's Battlefield 2 and Oblivion and GRAW, but is that it in the way of great 360 games? Nothing else really excites me yet.