I have a video screen saver program that uses .avi video files.  The
ones I want to use are .mov files, unfortunately.  Is there software
out there that doesn't cost and arm and a leg to change one video
format to another?

Hi there,

I've found a couple of free programs that can convert .mov into .avi.

The RAD Video Tools, which can be downloaded at
http://www.radgametools.com/bnkdown.htm, can convert nearly any type
of movie, graphics, or sound file into another format. I tested it out
to make sure it works, and successfully converted a .mov file to .avi.

Another method of converting the files, is by following step 2 (you
might need step 1, but ignore 3) of the following site (
http://www.divx-digest.com/articles/mov2divx.html ) to convert between
the two formats. This method of converting my test file worked as
well, but was more of a hassle then using the RAD tools.

Finally, I found out that it's possible to export a .mov file to avi
right from the Quicktime program itself if you have the registered
version. (File>Export). However, the quality using this method was
rather bad and took much longer to convert compared to the first two
ways.

Hope that's what you're looking for. If you have any questions about
this answer, please feel free to ask!

-Deadlychiapet-ga

Resources used:
DivX Digest - MOV to DivX Guide -
http://www.divx-digest.com/articles/mov2divx.html
Steve's Digicams - Forums -
http://forum.steves-digicams.com/Forums/viewmessages.cfm?forum=57&topic=5481
http://www.greenspun.com/bboard/q-and-a-fetch-msg.tcl?msg_id=003qap

Google search terms used:
mov to avi converter