We have a ceiling fan with a wall mounted remote. The light started dimming and brightening on it's own. :eek: In the past, the light would occasionally turn on by itself. Any clues what would be doing this?

Interference from something like a garage door opener or a neighbor. Try changing the code. Usually a dip switch in the canopy and the remote. You may have to recycle power.

KISS is correct. Change the frequency of the fan and remote. See:

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More