Do you like Action RPG type games with more of a hack and slash type gameplay style?
Lord of The Rings, Return of the King is a very fun game that is two player co-op same screen. I loved the game.
Baldur's Gate I and II are great overhead action/rpg games, too.
The ratchet and clank series are good.
How about shooters? There are a lot of great FPS/TPS games that are more on rails and less "sandbox". I can't stand sandbox style gameplay -- Grand Theft Auto, for instance...