DVDShrink is about the easiest route to backing up DVDs (and it's even one-click if you use Nero).
DVDShrink is no longer in development and it can't copy some newer DVDs due to the encryption schemes used.
For those that trip it up try
DVD Fab Decrypter and then run shrink on the ripped data.
DVDShrink will let you remove the extra scenes, language tracks, menus etc etc out of a DVD to make it small enough to on a single layer DVD (4.7GB). If the remaining bits are still too larger it can compress them to fit (or just compress the entire DVD if you so desire).
Since Shrink is a transcoder if the compression ratio is more than 80% or so the quality will suffer. So try to keep minimize the amount you compress the video.
Now if you absolutely
must compress the hell out of your data then try
DVD Rebuilder. It is a re-encoder and will deliver much better quality on compressed videos. Unfortunately the tradeoff is usually in the speed department, the free codecs included with Rebuilder will make the process slower than if you use Shrink. There are some codecs that are faster (CCE & procode) but they are proprietary and you'll have to pay for them.
So if you don't need to compress the video then it is easier to just stick with Shrink.
You can also use dual layer DVD-Rs so you don't need to tear out the menus etc or resort to compression, but they do cost more.
