Not sure what really counts as "rare"... and I've only been collecting games for a little while. But if other peoples' posts are any indication, I have
Golden Sun 1 & 2,
Fire Emblem PoR and RD, (and sacred stones if that's considered rare...?)
World Ends With You,
Tales of Symphonia (recent acquisition I found in a gamestore near my middle-of-nowhere college),
Twilight Princess for GC
Zelda Collector's Edition for GC
A black label copy of Melee for GC
LoZ: Four Swords Adventures for GC
Pokemon Colosseum and XD...
Used to have Sunshine, Pikmin 2, and Wind Waker for GC, but they were stolen, and I lost a crapton of other games all at once. :/
...those are what come up off the top of my head... I'd have to dig around for more. And I only got into video games when the gamecube/gba were a thing so I don't have much from earlier than that. D: