My ceiling fan turned on by itself. HELP!?

Are you sure somebody didn't hit the alarm on enabling the alarm function on the clock? Does the fan have a remote control unit to it? You might try changing the address to it if that is the case as a neighbor could be controlling it without knowing it. The fan could have a bad switch in it or the wall switch is going bad. There are possible explanations to what is happening other than a poltergeist.