There are many different games released on the Xbox 360, many of which feature co-op: the ability to play the game with a friend on the same console using split and sometimes shared screen. There are also games for two that you can only play from different consoles, over the network.
This list contains shooters, strategy, simulators, fighting games and other games for the Xbox 360 that feature local co-op or the ability to compete with your friend in split screen.