As far as I'm aware of, the free edition of Video DVD Maker (download page) does not watermark the DVDs it creates and will import video from AVI files and video sources (e.g. capture card). The limitations of the free edition include the inability to make DVD menus, create slideshows, use pre-rendered MPEG files and make advanced setting adjustments, which shouldn't be a problem if you're only interested in making a single DVD for each AVI movie.
[B]Edit:[/b] Posted too soon. First time I've heard of DVD Flick (website link), which looks like a much better free option