Wii for me as it had the best Mario, Zelda, Smash and Mario Kart versions upon release.
Also had new refreshing titles like the Wii series.

Switch versions have topped those versions though.(WiiU as well for Zelda and MK)

If we discount Rare as a second rather than first party developer than I gotta go with the Wii.

It had two of the best games ever made in Mario Galaxy 1 & 2, two great Zelda entries in Twilight Princess and Skyward Sword, Xenoblade Chronicles which combined accessible yet deep RPG gameplay with an unforgettable world and story, one of my top 2D platformers of all time in Donkey Kong Country Returns, one of the most purely fun couch multiplayer games I've ever played in Mario Kart Wii, some of the mind-blowing next-gen experiences I've ever had in Wii sports/Resort, and a wondrously immersive adventure in Metroid Prime 3.

GameCube had Two original zeldas, an open-world Mario, a debut Luigi, a debut pikmin, waverace, 2 original Metroids, plus a GB Advance adapter.

I agree with this. It's really difficult sometimes so if we go with everything Nintendo publsished then we would get a better picture, I guess. Think about Star Fox Assault or F-Zero GX from the Gamecube, what are they? They're obviously Nintendo games but they had been developed by Namco and Sega respectively while Nintendo did the publishing.

I can find great games on all of these systems, but I did vote for GameCube. Actually would say Switch is my favorite, but since it is not listed (understandable because the lineup is still growing), I went with GCN.

GCN has my favorite Paper Mario and Metroid games (TTYD & Prime 1). Excluding Switch entries, Wind Waker, Twilight Princess, Double Dash and Melee are some of my favorites from their series. Also gotta give a shout out to Colosseum & XD. Though I don't like Sunshine as much as other 3D Mario games, it was still a solid entry.

I ultimately decided on GameCube, but Wii is a close second.
Here's why I went with GameCube

Luigi's Mansion: So short, but I love it so much that I have played through it multiple times.
Super Smash Bros. Melee: I actually prefer Brawl very slightly, but Melee is amazing too.
Animal Crossing: An excellent game, and the first AC I played. It's better than Wild World and City Folk, but weaker than New Leaf and New Horizons.
Super Mario Sunshine: An amazing game
Mario Kart: Double Dash: One of my favorite Mario Kart games
Paper Mario TTYD: One of my favorite RPGs
Chibi-Robo: A fantastic game
Mario Party titles: 6 is probably my favorite Mario Party ever
Mario sports titles

Wii certainly comes close though, especially because it has three Mario platformers and a great game like Xenoblade Chronicles

Yeah maybe we can do a round 2 at the end of the Switch's life, I didn't think it was fair to include it while it's still a work in progress.

So far, for my personal tastes, I feel like Switch is above GCN and NES but still behind Wii U, SNES, N64, and Wii. Mario Odyssey and BOTW are incredible, and Splatoon 2 and Xenoblade 2 are very good too, but a lot of their published releases this gen are outsourced or recycled from previous systems. Still, they may yet have 2-3 years left to grow.

Doesn't the Wii play all those games anyway? Plus it's own library?

@Pemalite To be fair, the point of this thread is to look at each system's own lineup of games, otherwise I would have picked the Wii myself.

Exactly. That would be like giving the Wii U your vote because of the combined Wii and Wii U first-party games you can play on it.