I have most of the Zelda games for N64 but I wouldn't really class them as rare. I also have a few of the pokemon games, e.g. pokemon yellow, red etc. I know a guy who has a working copy of Zelda for the NES which I suppose is kinda rare.
I've got a Panasonic LaserActive system (LaserDisc game player in same console as a Sega Genesis, less than 1000 ever made) with Ghost Rush, one of the greatest games ever that nobody knows exists.
I'm not sure how popular this game is but Dragon Quest 8 is by far my favorite game. Its a semi old ps2 game with amazing voice work and graphics for being released in 04.