GC era Nintendo was pretty cool.
GC offered some really unique games, the console was tiny and still made of Nintendium, at an acceptable price range after the initial sales bomba. Wavebird was expensive as fuck but the best wireless controller of its time, and they attempted a first very timid and doomed to fail venture into "that online and local network gaming thing" with PSO and Mario Kart. Pretty good stuff from third parties as well, at least in the beginning. Still waiting for the rest of those Capcom 6...
Also, I really liked the tiny discs. Sure, they helped doom the system to lead a life of an also-ran due to their small capacity and bandwidth issues, but they were
tiny. Added an almost apple-like appeal to the thing, and seriously cut down on physical storage space requirements.
The horribly expensive and rare DTV cable though... what were they thinking.
And the hoops you had to jump through to make it work with some games. Cripes. Why wasn't that stuff automatic, or at least a setting in the (beautiful) UI.
Also, the ads and projected public image was very different to the Nintendo of today.
That said, I love Wii era Nintendo just as much. The software and hardware design philosophy was questionable at best (with devs publicly crying bloody tears about debugging etc, a braindead decision to hardcode internal flash memory size so it could not be extended in later revisions, no freaking digital audio for DVD playback, etc pp) but there are a whole boatload of great and unique games on that sleek slab of white plastic. No more Nintendium though, the damn thing was fragile, especially the first few batches...