Any of the games highly rated by collectors simply for being rare. Especially Gotcha Force and Battalion Wars.
I had people offer to buy Battalion Wars from me, but it was fun to have around just to show people who were convinced it was one of the best games on the cube, only for them to play it and find it to be utter shit.
In the spirit of the thread. Syndicate (the EA FPS), Far Cry 3, and James Bond 007: Everything or Nothing.
These games all had amazing co-op modes that nobody would play with me, and still don't.
Syndicate in particular was so brutal and the weapons so much fun to fire, and the missions were all very cyberpunk with missions like stealing servers from rival companies under the guise of a negotiation. You'd then unlock new tech for your weapons that made them all feel unique. Far Cry 3 had you playing as a group of horrible people that hated each other but worked together anyway. The way loot was tiered by storage device was fun. eg. Hard drive > flash drive, but took longer to unlock. Everything or Nothing had you playing as junior agents trying to earn 00 rank. I forget the story, but I think it was set before the events of the single player, and set up the events of the tutorial mission.
These were custom built, stand alone co-op modes, and in some cases (especially Syndicate) were better than the single player of the games they were attached to, but some people don't even know they exist.