I was pretty late to the party with this console, I think I only got it around 2005 because back then I was young and didn't have money of my own and as such I had to rely on the generosity of the adults in my family. I remember being excited about it ever since it first released, watching commercials for the console and games on TV, reading about them on magazines and even seeing them showcased in game shows, not to mention visiting websites and watching videos online before YouTube was a thing, needless to say I have very fond memories with the console, and when I got one, I really felt it delivered. Got a platinum one and I had to choose 4 games, and I went with Super Mario Sunshine, Melee, Wind Waker and Thousand Year Door. Loved Melee, Wind Waker and TTYD, even though I could never get around to playing TTYD in it's entirety a second time, and even to this day I'm bothered there never was a Wind Waker rerelease that adds back the cut content, and there might never be one. Despite loving those three games I was disappointed with Sunshine to the point I could never bring myself to finish it, I went in with high expectations though, but I ended up selling it. I eventually got around to playing other games besides the initial batch of four, mostly bought but one lent. Got Tales of Symphonia, Metroid Prime, Star Fox Adventures, Twilight Princess and Resident Evil 4, and borrowed Pokemon XD from a friend but gave it back to him after beating it. Wasn't too impressed with Pokemon XD but I much prefer the graphical style it went with than that of recent Pokemon games. Beat Metroid Prime and sold it to later get the Prime Trilogy on Wii. Enjoyed Star Fox Adventures despite it's bad reputation but I couldn't stand the voice acting in the game, eventually sold it but I kinda miss it, might buy it again someday, I dunno. Had fun with Resident Evil 4, beat it a few times but sold it expecting to buy one of the rereleases, which I still have to do, LMAO. Still keep ToS and TP despite both games having had rereleases, might sell TP after beating the Wii U version because I was somewhat disappointed with it as I didn't feel it managed to capture the feel of earlier Zelda games properly on top of being too easy, hoping both it and ToS are rereleased on the switch though.
Unfortunately I sold my Gamecube to be able to buy Brawl back in the day, but I would like to buy another one when I get the money for it. I eventually got other games on a trip to Europe, another copy of Melee for collection purposes, and also because it was cheap (only 15 euros, I assume it was because it was an NTSC game being sold in a PAL region), and a copy of Waverace, which I sadly haven't gotten around to playing, but that's partly because I don't have the room to put my Wii and Gamecube games right now, though I might try organizing my battlestation to free up some space soon.
I remember one time when I went to the game store and had to pick between Resident Evil 4 and Star Fox Assault and went with Resident Evil 4 because of the reviews, which was a good choice at the time, but the game went on to have many rereleases while Assault was never rereleased, I tried to buy it recently at a store which had it at a pretty decent price though, but by the time I got there someone else had already bought it. Sometimes I can't help but think about which games I could have gotten that are currently on my wish-list here over games that I wasn't too keen on or that got rereleases, but there's no reason to stop at exclusives, some multiplats had good versions on Gamecube too, better than those on the other consoles in some cases even.