Well, once or twice, my Wii-mote wouldn't turn on at the Wii channels screen.
Once, when my mom was playing Zelda, the plus button and the accelerometer in the Wii-mote wouldn't work, so we called Nintendo tech support, and he told us to turn the Wii-mote backwards and hit the Wii-mote on the palm of our hand (it worked, thankfully).
Finally, I was playing my own custom level in Elebits, when the game froze. I unplugged the AC adapter, and the reattached it. I turned on the Wii, and it worked perfectly.