Mirror's Edge
The game was absolutely stunning to look at doing parkour across the city was a blast. I never really had a problem with getting stuck on objects or not knowing when to jump due to not being able to see my feet like other reviewers complained about
It was a shame that a lot of the game had you confined to indoors though, and at certain parts playing without a gun was quite difficult but a sequel could fix these things (i dont think you should even be able to use guns in the first place, really)
EDIT: also
Sonic Adventure 2: Battle
This is how Sonic in 3D should be done. It had good variety, a sense of speed in the sonic/shadow levels, challenge, great soundtrack and of course the fucking Chao Garden <3
Super Mario Sunshine
I would argue the best 3D Mario game. Its inclusion of watergun-based puzzles and challenges was extremely innovative and fun. The problem was, it tried to re-invent 3D platforming at at time when it was still fairly new and fresh; it was before its time
Shadow the Hedgehog
People complained about its shallow attempt at making the series edgy and while I agree that guns were a silly addition, I think it was pretty good. I am a HUGE fan of back/origin stories and it was fun learning about one of my favourite characters. It was a bit difficult at times, but the 10 different endings (not to mention all the different paths you could take to achieve them) added loads of replay value.
To be fair, these last 3 were games I grew up with so I might be a bit biased, but years later I am still able to get a lot of entertainment from them
Also yes, I did have a GameCube, how did you know?