I'll add the Call of Duty games, particularly CoD 4. Mass Effect is also good, and since the Civilization games have already been mentioned, I'll throw in Civilization Revolution. It's a vastly dumbed-down Civ game for the Xbox360 in which you can finish a game in about 3-4 hours. I also like Battlestations Midway; even though it's unrealistic and pretty hokey, it's a lot of fun. The much bigger Battlestations Pacific is being released in a couple of weeks.
My favorite 360 game is GTA IV, and the add-on Lost and the Damned is fun too.