I've broken one Gamecube controller.
It was while playing the Rayman game on the gamecube.(hoodlum havoc IIRC)
The boss was fought on an arena surrounded by lava, the powerup required to beat the boss was on the side of the arena.
You have to climb down the side, get a powerup and back up while avoiding fireballs which make you fall in the lava. Of course, it's only fair if those fireballs follow you so when you fall in the lava and get back up the side, you're immediately knocked back down.
After 15 minutes trying to get out of the lava(restarting a lot, fought the boss for maybe 3 minutes), I got so angry I smashed my controller against the wall and gave up. A while later I noticed that the control stick didn't go back to it's default location and when I tried to move it, it broke off.