My top favorites would probably have to be Twilight Princess and Super Mario Sunshine. I know people say that Twilight Princess was not the best of the series, but honestly it's my favorite and first Zelda game I played. Super Mario Sunshine though, that game has so many memories tied to it for me it's insane. I wouldn't give my GameCube up for anything.
Oh, and Animal Crossing too! My parents put so many hours into that game with me.
Animal Crossing is also insanely popular. The gamecube had a lot of untapped potential, and a lot of unused hookups, that they could have used to expand the GC Animal Crossing into a fun game with online capabilities. Ditto on that comment for pretty much any multiplayer game for that system now that I'm thinking about it.
I absolutely loved played Mario Kart DD on Gamecube. One time, I was able to get 8 friends and two Gamecubes/TVs together for some LAN play. SO MUCH FUN. I just... don't care for online play. So impersonal. One of the best times I ever had was when we actually had 4 Xboxes and 16 friends playing HALO. The house was pack, wires every where, people shouting and cursing each other. You just can't replicate that feeling online. Well, the cursing and shouting is there... lol
Super mario sunshine is (in my opinion) the undisputed champion of all gc games. Nothing even compares to it other than I-Ninja, which comes to a close second. I will put the list here of my top 5 in order from worst to greatest of those 5.
5: Luigi's mansion
4: Pokemon XD, gale of darkness
3: Super smash Bros melee
1: Super mario sunshine
Ooo just down to 5? Well i will try.
1) Wind Waker. ITS SO GUUD
2)Twilight Princess. One of the most underrated Zelda games IMO
3) Smash melee. My second favorite smash game.
4)Pokemon XD gale of darkness. #UNDERRATED
5) Mario sunshine. Iz mario.
My absolute best game on the GameCube is Resident Evil 4, truly a masterpiece. Then there is the James Bond franchise, both the single and multiplayer game moods is very good and super fun to play with your friends. I especially like the bots feature where you can also engage AI controlled enemies who more or less are less have very similar behavior to actual players. I would like to pick favorites but every Jame Bond game on the GameCube is good.
I don't know about "best" games, but my favourite game on the Gamecube was Animal Crossing. There was something about being completely free to do whatever you wanted, while at the same time having a purpose - I loved it. I can spend hours and hours playing a game like that. Honestly, the other Animal Crossing games didn't do the same thing for me.
Wind Waker may have been my favorite Zelda game. I loved the graphics and soundtrack.
Melee is a game I can still break out a dozen years later and play with friends.
Double Dash for the memories of being the back seat rider with for my older brother (maybe not fun at the time, but it's funny to think of now).
Paper Mario Thousand Year Door because it gave me hours on hours of entertainment even though I never managed to beat the final boss.
Super Mario Sunshine, again for the hours of entertainment.
Man, it gives me some serious nostalgia looking back at all those games. They seem so much better than modern games, but maybe that's just the memories they're associated with.
Me and my friend used his gamecube pretty much exclusively for melee. There were lots of games in between, but none of them held us like melee. It was great, but I don't remember very much of anything else between it.