Very nice video, tho I prefer the N64 predecessors of Paper Mario and F-Zero.
The Gamecube was a very formative system for me, probably the one with the most nostalgic value for me growing up alongside the GBA, my top would be:
1. Tales of Symphonia. I have a lot of emotional attachment to this game, being the first RPG with a very captivating world, story and characters that I had the pleasure to play, I always make some time every year to give it a replay, still the top of the genre for me with memorable dungeons, well sized overworld, fantastic pacing and music, lots of funny moments between party members that oozes chemistry without being annoying, plus a lot of also smaller character moments that further cement their relationships and an incredible English dub that surpasses the japanese one, being one of the very few JPRGs to have that much effort put into the voice cast.
2. The Legend of Zelda: The Wind Waker. Was my favorite Zelda until Breath of the Wild, I adore its world and incredible sense of adventure, the music and artstyle really resonated with me. Also features one of the best Zelda stories.
3. Metroid Prime. Absolute perfection, the exploration, discovering the lore of the world through the scan visor is still such a joy to go through, also my favorite Metroid. The incredible atmosphere brought to life in its world design and music.
4. Baten Kaitos Origins. This is the only RPG to ever come close to fulfilling everything that I want from the genre since Symphonia, this one I only played a couple of years ago, but god damn, it reminded me of that time where dungeons in JRPGs had personality through simple but effective memorable puzzles, set pieces that remind me of the quirkiness of Mario RPGs, all tightly wrapped in a fast and engaging combat system and great story, that perfectly ties in with the original game.
5. Fire Emblem: Path of Radiance. Still the best FE for me, just a linear, well designed, fair, no filler strategy game, it does what it needs to do and is fantastic at doing that.
6. Viewtiful Joe 2. da best 2D beatem up/platformer, by not Platinum Games, back when it was Clover.
7. Kirby's Air Ride. Some say Double Dash, others GX, I say Air Ride. While light in content, City Trial is just the greatest mode ever made, I can get lost playing that mode for hours with just CPUs, is that freaking fun for a simple idea, racing a round a small hubworld, getting power ups and preparing for a final stadium event, is so weirdly addictive.
8. Luigi's Mansion. Just a nice, short and charming ride, is one of those games that I never get tired of replaying.
9. Pikmin. There is something very satisfying about using an army of carrots to defeat some weird creatures, while managing well your time to recover your ship parts, another game from a series I like to replay a lot in general.
10. Donkey Kong Jungle Beat. An incredibly creative platformer that works so well with a freaking bongo controller, is so weird and different for a Donkey Kong world and I love it for that.
11. Star Fox Assault. The gameplay might not be as tight as 64 or 2 for me, but I appreciate it for trying to build upon the Star Fox lore and give the characters continuity and development, Wolf becoming my favorite character from the series, all that without going for bad fanfic levels of writing like Command.
12. Custom Robo. Simple combat with a ton of customization options, quite like the game flow of the Robo games, they also have rather, dark storylines that come out of nowhere, which I can appreciate.