The Gamecube was a legit gaming system. Here's some off-the-top-of-my-head reasons:
-It had decent third-party support and hosted many of the major third-party releases that the Xbox and PS2 had.
-It was small and extremely easy to transport (unlike the Xbox).
-It was damn near indestructible (unlike the Xbox and PS2).
-It had a slew of great exclusives, including many that took people by surprise (Metroid Prime, Eternal Darkness, Viewtiful Joe, Resident Evil 4, Resident Evil Zero, MGS: The Twin Snakes, Phantasy Star Online Ep.1, 2, and 3))
-It was competitively priced.
-This last one is pretty subjective, but I consider the Gamecube controller to be the most comfortable gaming controller I've ever used. It wouldn't be great for a game that heavily relies on the triggers (like a shooter), but it sits in my hands just perfectly.
I think that a lot of people dismiss the Gamecube because, while it had some innovative games, the hardware didn't really do anything to stand out or innovate in its generation. PS2 doubled as a DVD-player and it was released at a time when DVD was still becoming normalized into every household. Xbox broke ground in mass multilayer gaming for consoles, both in LAN and online.