You should definitely add Resident Evil (1) remake for Gamecube. Fire Emblem: Path of Radiance and Beyond Good and Evil are must haves as well imo.
Other suggestions:
DKC 2: Diddy's Kong Quest (SNES)
Secret of Mana (SNES)
Chrono Trigger (SNES)
GoldenEye (N64)
Zelda: Majora's Mask (N64)
Skies of Arcadia (GC)
Edit: Reasons:
RE 1 is the 1st game of this amazing series and sets the standard. The game is creepy and very tough, ammo is very restricted as are save possibilities which makes this Survival Horror definition "hardcore to the max". The story development is great as well. And of course: shooting zombies!
Fire Emblem: Best Strategy RPG around. Very tough as well. Once characters die they'll never return. Storyline is amazing, characters very well developed.
Beyond Good and Evil: With Eternal Darkness and Okami probably the most underestimated (saleswise) game ever. Zelda-like gameplay, compelling main characters and a great story. Lots of humour in this game as well.
