The Nintendo Gamecube was my most played console of that generation.
I was 17 at the time working part-time getting ready to start studying IT at college later that year and had the gamecube pre-ordered for launch day and got Rogue Squadron 2 with it.
Rogue Squadron 2 was one of them games kind of like today with achievements except you got medals based on your performance. I think I managed to get silver/gold on most of the missions. It was a very replayable game for me except for those rare moments when a stray tie fighter would decide to kamakaze you ruining your score.
Some of my favourite games early on I played mostly in singleplayer as my brother was more into pc gaming at the time.
Games I spent a lot of time on were:
Super Smash Bros Melee
This game was a fun sequel to Smash Bros, didn't play this one as much in multiplayer but it had lots of unlockables.
Mario Golf Toadstool Tour
The sequel to the N64 game I played a ton getting all the birdie badges for a challenge in N64 magazine. This was a game I spent a lot of time playing when I was moving country in 2004 and not having internet for well over a year.
My first shmup on a modern console since Fire Shark on the Sega Megadrive. This game was hard but one of them rare difficult gaming experiences where I didn't get frustrated for dieing but wanted to keep playing. The training mode was fun to practice on with being able to slowdown the game and watch demonstrations of sections of the game. A missing feature I would have liked to have seen in its Steam release.
Soul Calibur 2
So many modes for singleplayer content... rarely played this in multiplayer but the wealth of things to do kept me playing this a long time.
Crusin' World USA
This simple racing game had things to unlock for completing races. One thing I enjoy in gaming is unlocking things and after a TON of racing I finally had gained enough EXP to unlock the Speed Demon car by the end of my time playing this game.
Final Fantasy Crystal Chronicles
This was a game I played purely singleplayer back in the day, my favourite thing about this game was the moogles. Was funny when your moogle companion would get cranky if you didn't take your turn holding the Chalice "It's your turn now, kupo!".
Resident Evil 4:
My second resident evil game, originally played resident evil 2 on the PS1. Played through this game many times and spent many nights when not playing it talking about it with friends in the visual lobby which brings me to my most played game on the Gamecube.
In the early days of the gamecube online gaming was just beginning for the generation of console gamers and I played a lot of single player games that was until the game I was very hyped for was released.
Phantasy Star Online Episode 1 & 2
This game is what started almost half a lifetime spent playing games online. To this day my adventures on PSO still continue online through the creation of private servers. It was a game where the community in the game gave me so many amusing memories and met a friend called Sam who I have played online games with for over a decade. It had a level cap that was so long to reach you could still be hunting for rare gear before you reach it.
With 2000+ hours alone on my FOmar Sonic Beta I never reached level 200. I got him to level 186 before a file corruption but playing the game with my friends was so much fun I had several memory cards which were used to make new characters with new ID's to level together.
The game had a system where different ID's based on your name would give you different loot so everyone hosting parties had potential for different gear drops.