Kameo has a co-op mode in it, and is a decent platform game.

Lego Star Wars II has full drop in drop out co-op support (but sadly no live support on the 360).

Beyond that, check out the arcade. All the games have demos, so you can see if they offer multiple player support.

I'd recommend looking into getting a Wii. It will let you play the GameCube games and also the newer Wii titles likely to be a blast multiplayer with your girlfriend.