Let's see...
Wii:
From the top of my head: Final Fantasy Fables: Chocobo Dungeon (I wish for a sequel someday), Rune Factory Frontier, Red Steel 2 (so much better than the first one), Zack & Wiki, House of the Dead: Overkill, Little King's Story, Opoona, or Resident Evil 4 Wii Edition (All the content of PS2, the better visuals of GC a bit improved, and three different control schemes make it still my favourite version of the game, Wiimote + Nunchuk is fantastic) are but just a few of the games I appreciate on the system.
When you stop and look Wii got a quite nice amount of fun stuff. It has also many tiny games like Marble Saga: Kororinpa or Geometry War: Galaxies, which are very simplistic yet really fun.
Gamecube:
Now this one got more "standard" third party support. Some of my instant favourites would be Viewtiful Joe 2 (1 is also awesome, but 2 has a bit more variety and extra content) and Gotcha Force (I didn't expect it to be SO addicting) from Capcom, Gladius (pretty decent often forgoten strategy RPG), Skies of Arcadia: Legends (ony of my favourite games all around), Super Monkey Ball 2, Sonic Adventure 2 and Sonic Heroes (I never played them until the seventh gen was ending, but man, I've been loving those two quite a bit) from Sega, and I've also put a rather big amount of hours on Ribbit King and SSX Tricky.
Beyond Good & Evil and Crazy Taxi are pretty good picks too, I never got tired of old priests swearing and doing backflips to leave your car and angry women asking you to take them to Pizza Hut right after you almost crash into them.
I could talk about games for both systems for hours.
