Some solid picks, and good vid! I often forget this console, while not exactly my favorite for most Nintendo properties, actually had quite a few 2nd and 3rd parties I really liked. 

Here's my own list if I were to make one:

1. Smash Bros Melee
2. Eternal Darkness
3. Tales of Symphonia
4. Metroid Prime
5. Resident Evil 4
6. F-Zero GX
7. Pikmin
8. REmake
9. Zelda: Wind Waker
10. 1080 Avalanche
11. Super Monkey Ball
12. Soul Calibur 2

* I'd probably put Zelda Twilight Princess on there but I consider that more of a Wii game as it's the console I played it on.

Twilight Princess is my favourite, so had to vote 'other'. A note on some big omissions: I never got into the Metroid Prime trilogy much - I'm sure I'll get round to properly immersing myself in them at some point. Mario Kart DD is one of the few titles in that series I've never played. Smash Bros, I played a fair bit of multiplayer, but I've never really warmed to the series like a lot of people have. My full list of 12.

Twilight Princess
Wind Waker
Super Mario Sunshine
Resident Evil 4
Resident Evil Remake
Eternal Darkness
Paper Mario: The Thousand Year Door
F Zero GX
Tomb Raider Legend
Star Fox Adventures
Sonic Adventure 2
Turok Evolution (I have a lot of love for this one)

Shout out to Geist, XII, Sphinx and some others I probably forgot.

Let's see.

1. Star Wars Rogue Squadron 2 - Rogue leader. Not just my favorite Gamecube game, but my favorite game from the whole generation. Gorgeous for the time with several of the levels like the Death Star and Hoth still looking good today, nearly 20 years later. Short but with incredible replay value.

2. Smash Bros. Melee. The reason I got a Gamecube. Even if I prefer some of the later games in the serie, Melee was something truly special and my introduction o many Nintendo franchises.

3. Wind Waker. Not my favorite 3D Zelda and the pacing in the last few hours is horrible, but overall a very fun and charming game.

4-5 Metroid Prime and Resident Evil 4. 2 Great games I only really got into on the Wii because of that system's amazing pointer controls.

Beyond that it's hard to rank. At the time I was more into games from familiar properties like Two Towers, Batman Begins, or Ultimate Spider-Man.

Yeah I’m also having a hard time with that. Obviously I  could mention Sunshine and Double Dash in a top 12, but they wouldn’t be there because I thought they were great, just because I can’t of anything that’s better. Especially if I’d discount Twilight Princess, it becomes a tough task.

Luigi’s Mansion was good though, that’d be my favorite at least.

I absolutely love the Gamecube so it's really tough for me to narrow it down to just 12 but here goes.

1) Smash Bros Melee
2) Resident Evil 4
3) Metroid Prime
4) Zelda: Wind Waker
5) Super Mario Sunshine
6) Pikmin
7) F Zero GX
8) Eternal Darkness
9) Soul Calibur 2 (the best version!)
10) Timesplitters 2
11) Luigis Mansion
12) Mario Kart: Double Dash

Honourable Mentions (if it were to be a top 20):
Prince of Persia: SOT, Mario Kart DD, Viewtiful Joe, Super Monkey Balls, Rogue Leader, Bloody Roar Primal Fury, Mario Party 4 & Sonic Mega Collection.

Extra Comments:
Twilight Princess would make the list except I own it on Wii not GC so it should be on another list. Also Paper Mario TTYD might do as well - I've heard great things yet sadly not played :/ it's really expensive in the UK!

Bullet shooter from hell. Ikaruga deserves in top 20.   Of course Paper Mario last great paper Mario deserves in top 10

1. Resident Evil 4.
- My favorite game. Of all the versions I have played only the PS2 version is worse and I like the Wii version best, but this is still the best game on the cube.

2. The Legend of Zelda Twilight princess
- The most complete Zelda game. Once again I think the Wii-version is superior but having Link left handed feels more correct.

3. Mario Kart Double Dash!!
- The best Mario Kart with the best battle modes. Shine thief and Bob-omb battle is not topped yet. The ability to avoid red and even blue shells with advanced technics (without using bugs or the like) make it the Mario Kart game were skill is much more important than luck imo.

4. Super Smash Bros Melee
- Phenomenal party-game. Phenomenal competition game. This celebration of Nintendo history is one lucky accident and the main reason for my forth purchase of a Nintendo Gamecube controller.

5. Donkey Konga
- Before guitar hero was a thing this music game with strange controller jammed in my bedroom. I cannot pinpoint what I love so much about it, but since I spent around 500 hours playing, it did something ight for me.

6. Eternal Darkness: Sanity's Requiem
- Long after I understood the sanity effect this game stunned me with its strange behaviour. The engaging story and atmosphere rose above its chunky controls.

7. The Legend of Zelda the Wind Waker
- Far from my favorite in the series, but long after the release this game still looks and plays great. Few games age this well.

8. Starfox adventures
- The only Starfox game I enjoy. I never have enough scarabs and prefer my feet on the ground.

9. Fire Emblem path of radiance
- Missing the charm of the GBA game that I adore. With its emotional power this strategy RPG is still very memorable.

10. Luigis Mansion
- Fun little game, bit short and a little slow to play. Humming the main theme and shouting for your brother is gold.

11. Super Mario Sunshine
- Colorful and charming and the worst main line Mario game. A little less watergunning and a little more plattforming please.

12. Metriod Prime
- King of atmosphere. Ambient music and the best looking game on the system. I never like the first person view and stopped playing pretty soon, but still listen to some of the music.

I'm so glad that somebody mentioned geist. Sure it was flawed but it was such a great game. I just wish it got some more dev time/publicity so it could have become a series. Unfortunately it will probably never be seen again. 

Geist is an underrated gem! It actually appeared on one of my earlier "Pick 60" episodes. It's too bad that n-Space folded, even though the quality of their output had waned in later years.

Yes!!! I haven't played Ikaruga in years (my buddy had a copy in high-school). I remember the endless sweet, sweet frustration :D

Mario Party 5
Mario Party 6
Smash Bros Melee
Mario Kart Double Dash
Super Mario Strikers
Super Mario Sunshine
Animal Crossing
SSX 3
Burnout 2
The Sims 2
Resident Evil 4
Need for Speed Most Wanted