Pikmin 2. 50 challenges you can defeat with two players. A brilliant game that's lots of fun.
Timesplitters 2 - It has an entire co-op mode, a great shooter that you can't NOT have fun with. Oh, not an FPS? Well nevermind then, but you're really missing out.
Tales of Symphonia is playable with 1-4 players, but that might get boring for the players that aren't the main player.
As was already mentioned, The Legend of Zelda: Four Swords Adventures is a perfect co-op game.
Mario Kart: Double Dash can be played co-op I guess, with the two people on one kart mode, which can be really fun and hilarious, or boring depending on the people playing.
I'm sure you can find some co-op things to do in Super Smash Bros Melee as well.