Co-op games are in notoriously short supply. I happen to know of some of them, because I seek them out myself.

Borderlands
Rainbow Six Vegas 1/2
Dynasty Warriors 6 Empires (local only)
Halo series is tried and true, and Halo Reach is supposed to have some very impressive co-op play (but you probably already knew that...)
Smash Bros Brawl has a good co-op story mode
Portal 2 is going to have a co-op mode when it comes out
C&C Red Alert 3 has a co-op multiplayer campaign

If you're on the Playstation Network, you can see about some of the downloadable titles-
Comet Crash (up to 3 player cooperative tower defense game - but local play only)
Monster Madness (Gauntlet meets Zombies Ate My Neighbors, up to 4 players)
DeathSpank (2 player local)

Older games:
Gauntlet series (I recommend Gauntlet Dark Legacy myself, you can find it on the Gamecube)
Alien Syndrome for the Wii (technically capable of 4 players, but I recommend no more than 2...)

I'll add more if I think of them.

what kind of game?

All depends on your preference...third-person, first-person, RTS?

Lets play Sven coop again :3 And finish off Half Life decay. We STILL Haven't finished that :< We could try Quake 4 Coop. I linked you info about it but I need to test on if it all works or not..cause I sorta don't have a full copy of it...so it'd be a bit of a pain to have to reinstall it after finding out it isn't gonna work for me. D: Also Killing Floor. You, me, skonk, maybe q.

I just had a good number of suggestions on that very subject, actually!

http://www.furaffinity.net/journal/1710973/

Left For Dead series is very good co-op.

Left 4 Dead 1 and 2 are good. 2 is lots of fun but 1 has the advantage of being cheaper and the availability of lots of third-party maps, though those can be hit or miss. If you go by ratings and feedback you should be able to pick out the good ones.