In no order....
Halo 3 biggest tournaments and prizes and fast paced, best Multiplayer Game online so much shit you can play, don't have to wait long in Matchmaking, can even make your own maps, play with a homie on the same console Campaign or Online in a shit load of categories.
Call of Duty 4 Modern Warfare, most realism in a FPS great storyline and Multiplayer is fun as fuck. Addicting Gameplay with modern weapons.
Fallout 3 best single player game out, can switch to 3rd person view too, has Action/Strategy/RPG elements in a big ass World where whatever you do changes the scale in the game. If you don't have Xbox Live yet this game is perfect because its not an Online game, but its deep.