So a friend of mine has the Dolphin Emulator, which can emulate GCN games flawlessly. He wants to know some good games, aside from Mario Sunshine, SSB Melee, and Rogue Squadron to download.
Well, some games that I really enjoyed and to the best of my knowledge were not re-released on later systems:
Viewtiful Joe 1 & 2
F-Zero GX
Super Monkey Ball 1 & 2
Mario Kart Double Dash
A couple that I heard very positive things about but never actually played:
Paper Mario: The Thousand Year Door
Eternal Darkness
And some that were originally on Gamecube, but got re-released on other systems which may be the superior versions:
Metroid Prime 1 - 3
Resident Evil 4
The Legend of Zelda: The Wind Waker & Twilight Princess
Prince of Persia: The Sands of Time
Pikmin 1 & 2
Metroid Prime 3 made it to gamecube? Shoot, I gotta find that version. From my knowledge, the Metroid series, like so, so many other franchises, got hit hard with motion control and became an absolute mess. I stopped playing it because the controls were just so, so bad. Anyone else remember Dragon Quest Wii? Kinda like that.
I can firmly recommend Metroid Prime 1 and 2, Wind Waker, Mario Sunshine (I don’t get people who dislike this one; while it’s no Galaxy, it’s still an incredibly solid 3D mario title), and SSX 3. All an absolute blast to play. 
I’m closing this since, as far as I know, using an emulator to play games is illegal.
I’m going to add on another note. I’ve been told from some that emulators are not illegal just as long as you own the games (on disc), but there are emulators that are illegal and when you use the word “download”, as you did in your OP, that makes me know that you’re talking about the kind you find online (that come in ROM form) that you don’t pay for and thus, are illegal technically…so this topic will stay closed.
However, if I remain in the wrong, feel free (anyone) to PM me again and/or make a topic in ATMB and I’ll hear you out.