Fantastic console, and the one that got me back to serious console gaming again after pretty much skipping a generation. (I later caught up on N64 and PSX). It is still the console where I have the largest gaming library, probably around 50 titles.
Wind Waker was awesome, SSB Melee was the best party game ever (4 controllers for the win), and I enjoyed getting the living crap scared out of me with REmake, RE:0 and Eternal Darkness. Later came the action culmination of the generation with RE:4.
It also had Metroid Prime 1 and 2, games that are close to perfect, especially MP1. The only real letdown of the generation in terms of "franchises" was Super Mario Sunshine, which, while having some great platforming, was at times more frustrating than fun, and I actually broke my first GC controller smashing it against the table after a particularly annoying part of Sunshine.
It also had a gem Viewtiful Joe, which is one of the coolest games ever, sadly the franchise never caught on with the general public.
Finally not to forget Twilight Princess, if you are purist, you do _not_ play TP on Wii with everything mirrored. Too bad there was no widescreen option on the GC version, and some slowdown in the city especially.
Special mention:
Soul Calibur 2
Rogue Squadron II
Beyond Good and Evil
Pikmin
Paper Mario
Super Monkey Ball!
The Wavebird controller (most comfortable controller that will ever be made)
F-Zero GX (fastest game EVER?)