I gave away my games a while ago, but I had quite a few rare ones.
A ton of NES games that were rare. I think the rarest was one of the Teenage Mutant Ninja Turtles games, I had all of them on the NES. Traded it to Funcoland for like $10 well after the hey day of the NES.
On n64, I had Sin and Punishment, which wasn't a very common game even in Japan.
On Dreamcast, I had Shenmue 1 and 2, Illbleed, Seaman, D2, and quite a few other semi rare games, although Dreamcast games never really gained much value.
On Xbox, I owned Steel Battalion (with controller) and Marvel vs Capcom 2.
Not sure if I had any rare Gamecube games...maybe Puyo Pop Fever? Also both Zelda collections, Zelda Four Swords, and Pacman Vs.
I had the 32x and a few games for it, and they were all fairly rare. I had the Dreamcast broadband adapter, which was really rare.
On Playstation 1, I had Xenogears and Breath of Fire 3...
SNES I had Earthbound in box with guide.
And then the idea of a rare game doesn't really seem to exist on current platforms...
From racketboy.com, here's some valuable (but not necessarily rare) games I also owned:
Ms. Pac-Man on the NES (the illegal Temco one I think)
The original Pokemon red for gameboy. (not rare, but apparently valuable)
Also for Gameboy, Legend of Zelda: Link's Awakening DX, Pokemon Yellow, Super Mario Land, Teenage Mutant Ninja Turtles, Super Mario Land 2, Metal Gear Solid, Pokemon Gold
SNES: Earthbound in box, Super Mario RPG
PSX: Xenogears
N64: Sin and Punishment, Conker's Bad Fur Day, Super Smash Bros, Ocarina of Time, Mario Kart 64, Paper Mario, Mario Party, Super Mario 64, Space Station Silicon Valley
Dreamcast: Marvel vs. Capcom 2, Power Stone 2, Skies of Arcadia, Shenmue 2
Gamecube: Phantasy Star Online Episodes 1 and 2, Metal Gear Solid: The Twin Snakes, Pikmin 2, Legend of Zelda Ocarina of Time / Master Quest, Legend of Zelda 4 Game Collection, Eternal Darkness, Super Smash Bros Melee, Killer 7
Xbox: Marvel vs Capcom 2, Steel Battalion with controller
Had quite a few on PC that were rare, like Panzer Dragoon, and maybe some older games like Master of Orion 2. But rare != valuable, and no one seems to colelct PC games.