I've finally got a current-gen console, and I chose the 360.
SO, Mercenaries 2: Fun, actually. You get to hijack stuff, and pretty soon they'll have Obama and Palin as an unlock.
Saints Row 2: Like Grand Theft Auto, but better. They DROWN you in customization features, but the game doesn't force you to learn everything in the beginning. You just jump right into the action as soon as your character is created.
Dead or Alive Xtreme 2: Erotic. 'Nuff said.
Halo 1: Do I really need to write everything? It's no difference for the Xbox than it was for the PC, except it has Co-op but no online.
Kung Fu Panda and Lego Indiana Jones also came with the system, and those games are pretty alright.