There were a bunch of GameCube games that I missed out on for various reasons, and I'm making up lost time with many of the games through emulation means. Sorry, i'm not scouring through eBay for ridiculous prices that won't even support Nintendo in the end, and until Nintendo supports GC games in VC, that's my current method.

Currently playing through/planning to play...

Fire Emblem: Radiant Dawn

Paper Mario: TTYD (I think I only played part of it, don't think I've actually beat the entire game)

Super Monkey Ball 1-2 (lol)

Luigi's Mansion

I take great pleasure from puzzle and platforming games, but I generally like most genres.

What are your suggestions?

You can play gamecube games on the Wii U with a bit of fiddling. Youtube is your friend.

As for games:

Mario Sunshine
Tales of Symphonia
Skies of Arcadia
Metroid Prime

Viewtiful Joe

If you can get past the atrocious voice acting, Star Fox Adventures is a nice little action adventure game. Kind of a Zelda-light. Speaking of which, if you haven't played Wind Waker, I would obviously recommend that. If you like fighting games, Soul Calibur II is a ton of fun for noobies and vets alike. Star Wars: Rogue Squadron is also pretty incredible, if you have any interest in Star Wars or flying games.

Eternal Darkness. Rouge Squadron 2.

I really liked Resident Evil 4 on that one... Gladius I played on the Xbox but it is also on the gamecube and is rather overlooked imo

Eternal Darkness

F Zero GX

Pikmin

Baten Kaitos, both of them. Star Fox Adventures (don't listen to today's critics, atm critics loved it and so did I), Ikaruga and Wario World.

I think Gotcha Force is a pretty cool title for the GC. It has a collecting aspect like pokemon and you battle enemies in a 3D space. You basically play in a world where kids get toys that can fight each other, you can team up with people, and beat the enemies, and collect those enemy toys to add to your collection to then use for yourself in battle. It becomes very customizable with the amount of characters available. It's def one I enjoyed in college xD

Wind Waker and Twilight Princess
Metroid Prime 1 and 2
Chibi-Robo!