I have an unopened copy (still in the shrink wrap) of Pokémon Mystery Dungeon Explorers of Darkness. It's been over 7 years, and it still hasn't gone up in price
The rarest game I have is not exactly a rare game, but a rare collection of games. Specifically, the Legend of Zelda Collector's edition disc for the Game Cube - which has the first two Zelda games, plus Ocarina of Time and Majora's Mask, and some Wind Waker sneak previews (the disc came out before Wind Waker did). It came with my Game Cube when I got it several years ago, and I haven't seen too many around since.