I'm surprised barely anybody mentioned TTYD here. It's definitely at the top of my favourite games i've ever played, and I felt it had the perfect mix of combat, puzzle solving, and storyline. I've yet to see another turn based RPG that I enjoyed more than TTYD, and I still occasionally replay the game even to this day, just because of how fun it is.
Sonic Adventure 2 was also one of my favourite games growing up. Although it doesn't hold up too well these days, the Sonic and Shadow levels are still good fun and i'm still waiting for Sega to implement another Chao garden in their sonic games.
As for my gamecube itself, I own the silver one along with the emerald blue and spice controllers, which i'm really proud of owning, and they're still in an acceptable condition to this, albeit the sticks being loose (which is unavoidable) and a couple of scratches here and there.