I love the gamecube. its by far still my most favourite console. It was much easier to carry around than the PS2, and a lot of the best PS2 games didn't come out until the nearing end of that generation whilst the gamecube had experienced brilliant games throughout its lifetime.
The gamecube has so many of my childhood hours spent on it (this part of my childhood being just after my 9th birthday up til just after my 13th, however, it has continued to recieve a lot of love up to even now as a 17 year old).
I've have fond memories of games such as
Pokemon Collosseum
Harvest Moon: a Wonderful Life
Final Fantasy: Crystal Chronicles
Super Smash Bros. Melee
Megaman Network Transmission
Fire Emblem: path of Radiance
Ikaruga
Tales of Symhonia
Paper Mario: the thousand year door
Legend of Zelda: Windwaker
Pokemon XD: Gale of darkness
Mario kart: Double dash
Legend of Zelda: Four-sword adventures
(The) Mario Party (series)
(Sonic Heroes, Shadow the Hedgehog and Resident evil 4 aswell, but those also came out on PS2 at the same time... but i much prefer playing them on GC regardless

)
and this is without stating the many re-vamped remakes such as the Resident Evil Series and the Metal Gear Solid: Twin Snakes, which are also brilliant.
maybe i am just very bias though, i spent so many hours with my friends on so many of these games and would not have traded a minute of it. Sure, i've had fun with the PS2 and maybe thats even getting more use out of me at the moment (My friend had Persona 4, one of the few games worth playing left to be played by myself... also i need Shadow of the Collosus) yet i still have sunk so many more hours into the Gamecube... its just a brilliant console.
EXTRA- and i can still think of many games on the Gamecube i would love to play: the metroid trilogy for a start, Mario Sunshine... yes, i love the gamecube but have actually never played mario sunshine

see how much more i've yet to experience!