Is there a program that will randomly change the background on my desktop, similar to a screen saver program?

yes. lots of them. here is one of dozens (there are tons of other features with it too):

http://www.tucows.com/preview/418069

Here are some shots of the program in action and the little calender it can display on the desktop:

http://www.abf-soft.com/wallpaper-changer/screenshot.html

Thanks Shifty, I'll check them out.

Thanks Shifty, that is just what I was looking for.