My new Harbor Breeze ceiling fan light comes on at various time by itself. I have tried taking the batteries out of the remote and that doesn't change things. The remote does work correctly. How do I keep the light from turning on by itself?

Change the frequency of the fan and remote. See:

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-remote-controls.php)