I have a relatively small Gamecube library, but nevertheless I have some really good games in it.
Favorites (Off the top of my head):
- Luigi's Mansion: The very short "spooky" experience starring Luigi. A longer game (around the length of Luigi's Mansion 3) would have made it better, but may have led to some repetition. It is goofy and has great mechanics, great controls, an emersive setting, and the whole game is just fun.
- Mario Kart Double Dash: The Mario Kart for the Gamecube, simple enough. Great characters, great tracks, solid controls, good music, and a good battle mode. The Special Items idea was very interesting, but the whole "two characters per vehicle" thing never really hooked me. Overall a great multiplayer experience.
- The Legend of Zelda: The Wind Waker: An interesting cartoonish take on the series, with an interesting idea of traveling the seas and exploring various islands. This can be rather boring, as sailing can take a long time, but nevertheless the game as a whole is a fun experience worthy of this spot.
- Paper Mario: The Thousand Year Door: Although I do like the original N64 game a tad better, it is still just a super fun Mario RPG experience worthy of its praise. The writing is great, the mechanics are fun and intuitive, and the world the player is put in is really... something unique.
- Super Smash Bros. Melee: This one needs no explanation.
I would also like to mention that Super Mario Sunshine can be fun at times, but I feel that it is too experimental with various mechanics, leading to boring and really frustrating levels and/or missions. Therefore, I disagree with your opinion on Sunshine.
I don't actually have a lot of history with the GameCube because it was released in that time period of my life where I wasn't able to get new consoles. That being said, the few GameCube favorites I have are Metroid Prime 1 & 2, Paper Mario 2 and Tales of Symphonia.
The Mario Party games are easily my favorite, despite the inconsistent quality. I've had lots of great family time with them and every now and then I still bust out my Wii to play them.
I used to enjoy Kirby Air Ride's City Trial mode as a dumb casual mode, but I've squeezed out every last drop of enjoyment and it just bores the crap out of me now—and it didn't help that I already felt the game was pretty mediocre, only good as a laid-back thing to do in the background while chatting and stuff. I feel the same way about Phantasy Star Online: it's another game that I have many fond memories of but the idea of playing has no appeal to me anymore. Mario Superstar Baseball had an amazing, diverse roster that's only matched by its direct sequel. It's something I played countless hours of and always loved playing. I'm disgusted that this series hasn't had a proper new entry since the Wii.