-(if you haven't got a Gamecube before) 1st. Metroid Prime Trilogy
2nd. Donkey Kong Country Returns- 2D platforming at best; New Super Mario Bros Wii if you want something easier.
3rd. Super Mario Galaxy 1/2- 3D platforming
For multiplayer: Mario Kart Wii & Super Smash Bros Brawl
Don't miss Zelda: Twilight Princess and Monster Hunter Tri
Other games I can suggest are Metroid: Other M , Silent Hill: Shattered Memories , Muramasa: The Dragonblade , Sin & Punishment 2 , Tatsunoko VS Capcom , Punch-out , Red Steel 2.
And if for some reason you haven't played those yet Resident Evil 4 and Okami are must-buy.
^^^great list. I would also look into WiiWare games such as the Bit Trip series, lost winds series, Dr. Mario Online and reloads of Mega Man, Sonic, Castlevania and Contra. Smeags' recommend list gives a good listing of those.
If you haven't played legacy games, I highly recommend Super Metroid (SNES), Punchout!!! (NES), Megaman series (NES), Ninja Gaiden (NES), Zelda II (NES), Kid Icarus (NES), Final Fantasy (NES), Zelda OOT (N64), Mario 64 (N64), Super Smash Bros (N64), Super Mario World (SNES), Super Mario 3 (NES), Zelda: a Link to the Past (SNES), Castlevania II: Simon's Quest (NES), Super Mario Bros. 2 (NES), Paper Mario (N64), Kirby 64, Donkey Kong 64, Pilotwings (SNES), Sin and Punishment (N64), Excitebike 64 and Ogre Battle 64.
On Gamecube, you want to play Smash Bros. Melee, Resident Evil 1 (Remake), Prince of Persia series, Legend of Zelda: Wind Waker, Tales of Symphonia, Super Mario Sunshine, Metroid Prime, Beyond Good and Evil, Ikaruga, Donkey Kong: Jungle Beat, Pikmin Series, Legend of Zelda: Four Swords adventure and Waverace: Blue Storm.