Little Big Planet is one of the best free games being given away in the PSN Welcome Back Package. Its a blast with a friend online. You may also like Wipeout HD online if you enjoy racing games. The vehicles also have added weapons in the Fury HD expansion pack which is included. InFamous is an excellent single player game, no multi. Dead Nation I really enjoyed too, which is a top down zombie shooter two player online. Finally SuperStardust HD is single player online only, its an arcade analog stick shooter. Local has 2 player co-op.
If I had to choose just 2 for online it would be Little Big Planet & Dead Nation. If I was going off my favorite of the lot I would pick Little Big Planet & inFamous.
Trine is great on PSN if you have a local co-op buddy. Unfortunately not online co-op, but the sequel Trine 2 will have it so keep and eye out for that game later this summer!
Finally if you are looking for a none PSN online co-op game, my favorite online co-op game is Resident Evil 5. Also I really like Portal 2.