Hmn, this is a bit hard to judge for me since I don't keep tabs on how valued games are as I don't plan to sell any particularly.
If I had to take a swing at it, I'm pretty sure White Day: A Labyrinth Named School would be there. It's a obscure Korean horror game which a friend got for me in very good condition, and I hear the game is extremely rare due to it's obscure nature and Korean-only release.
Huh, I have hundreds of games and I'm sure some of them are rare but as of now as someone who doesn't look into these things that much I wouldn't be 100% sure which of these games I own are super rare and which only moderately. I own some old Dreamcast and SEGA Saturn games still, and unfortunately sold a lot of my old collection before I made the resolve to not sell my games if there was ever even the slightest chance I might want to play them in the future.
Decided to look up Gamecube games for an example, and from several articles of "rare Gamecube games" I do own Phantasy Star Online Episode 1 & 2 Plus, Cubivore, Legend Of Zelda: Collector’s Edition, Metal Gear Solid Twin Snakes, Ikaruga, Pikmin 2, Resident Evil Code Veronica X, Resident Evil Zero, Beyond Good and Evil, and Dance Dance Revolution Mario Mix. Are those really that rare? I would think some of these other games would be more so.