DVD Shrink works very well for me for backing up movies. Just make sure it compresses the output to within the capacity of a 4.7GB DVD. I use Nero to burn the output from DVD-Shink afterwards. Just be sure to stick DVD-Shrink's output in the VIDEO_TS folder in Nero.
DVD-X-Copy is suppose to be a DVD backup package as well, but it seems rather strange that it is ruining DVD-R's on you. Then again, I have not tried it so far.
From what I recall, Clone DVD is suppose to be used for making identical copies of data DVD's; like its predecessor Clone CD. I don't think it can make copies of CSS protected DVD movies or even recompress dual-layer discs down to DVD+/-R size.
If you can get DVD recordables handy, it may be worth getting some rewritable discs as well. They generally have similar compatibility as with the single write 'R' discs, but you can erase them at a later stage. Even you you don't use them for storing movies, they do an excellent job for backing up several Gig of data