UNIVERSAL: Dungeon Explorer I & II are probably the most fun I've had in old-skoolness.
ME: I've had a blast with Wonderboy III (Monster Lair), but both people need to have skills to get far. Same goes for Buster Bros., which is lots of fun.
MENTALLY CHALLENGED (ME): I've had a stupid amount of fun with MotoRoader. I suppose you need to get a bunch of folks together and see if they dig it.
AeroBlasters is the shoot-em-up I've had the most fun with playing 2-player co-op (you have a special weapon when working together!m), but both folks should be decent skill-wise, otherwise you just eat through continues.