Is there a free program that will download videos from YouTube and other sites?

yes there is I've done it. Found on google. don't remember the name though?

KEEPVID.COM

I think Youtube has a "Youtube" downloader.exe as well.

Try DVDVideoSoft.com: Download free DVD, iPod, YouTube video converter and editor software and freeware (http://www.dvdvideosoft.com/index.htm)

I use their youtube to mp3 converter for music.