As an owner of a GameCube, I can tell you this:
1) The controller sucks for fighting games or anything that requieres an intense use of the D-Pad or switching quickly from pressing button "B" to button "Y" or "X". (like, for example, Mortal Kombat: Deadly Alliance or Tony Hawk series)
2) Practically zero online games. I'm mean c'mon, there is a modem, yet no online games in America besides PSO. How about Splinter Cell or something?
3) Practically zero LAN games. Only Mario Kart. So ok, I understand that maybe developers do not want to mantain servers and all that online stuff. How expensive or hard could have been adding LAN support?
4) Lack of third party support. Even MS, a relative newcomer to the industry, managed much better support than veteran Nintendo.
Still like my Gamecube, though.