I collect retro games, and have a pretty big collection (many of them boxed) and many of them can be considered rare so I won't mention them all. But from the top of my head, some of the rarer games I own include:
Wii:
Metroid Prime Trilogy
GCN
Ikaruga
Baten Kaitos Origins, Eternal wings..
Pokemon Box
Zelda collectors edition
N64
Conkers bad fur day
Banjo Tooie
SNES
Chrono Trigger SNES (it never released here in Europe)
Mario RPG legend of the 7 stars (same as Chrono Trigger)
Secret of Mana
Secret of Evermore
Terranigma
Harvest Moon
NES
Probotector (contra)
PS2
Shadow of the Colossus (it's rare in Europe)
Suikoden IV
PS1
Suikoden
I also own a bunch of Japanese important games which would be considered rare in the west, including the Japanese only Fire Emblem games, Famicon Wars and Captain Rainbow
Spending warm summer days indoors
Writing frightening verse
To a buck-toothed girl in Luxembourg
NES, SNES, N64, GC, Wii, WiiU, GB, GBC, GBA, DS, 3DS, Mega Drive, Game Gear, PS1, PS2, PSP, XBOX 360, Atari Lynx