Pretty sure Crackdown has co-op modes for both on and offline. Same goes for Marvel Ultimate Alliance.
My problem with those and many other co-op games is that there's not actually a lot of cooperation. With Crackdown in particular friendly fire is a real problem.
If you have a lot of friends, I highly recommend Team Fortress 2 in the Orange Box. It's a brilliant class-based tactical game. Instead of utterly pointless deathmathces--the enduring appeal of which makes lose hope in humanity--you have objective-based goals that actually reward cooperation.
You've got classes that all reward different strategies and skills. If you're a twitch gamer, play a super-fast scout. If you're the sneaky tactician, play a sniper and find a nice high point or sneak behind enemy lines as a spy. If you're the patient planner, play an engineer and set up that auto-turret. If you wanna blow stuff to pieces, you have oh-so-many choices: a demoman's grenade launcher or a solider's bazooka or a heavy gunner's minigun or a pyro's flamethrower--all with their own individual strengths and weaknesses.
The only downside is finding good peaple to play with. If you have Halo deatmatch junkies, then they'll just run around solo trying to get the drop on enemies until they get killed, then respawn and do the same damn thing over again--all the while ignoring the mission objectives. If you have a bratty kid who just wants to mouth off into his mike, you can't do anything about it.