I play these on a NES emulator against my brother:
North & South
Ice Climber
Super Off-Road
Spy Vs Spy

I wouldn't put any of them on a "best game ever" list, but for multiplayer madness they are cool. My list would be something like this:
Zelda 3 - A link to the past (start with this and then do the rest of the Zeldas)
Super Mario World (start with this and then do the rest of the Marios)
Half Life, then HL2 (then spend 8 years playing CS online :P)
GTA (you might skip the first two but personally I love them)
GoldenEye 64
Mario Kart 64 (or any other mario kart, this is my favorite though)