A free alternative to AnyDVD is DVD43
which works in the same way - not as updated as AnyDVD so any really recent copy protection scheme will probably confound it, (and basically there really is only one DVD copy protection that can be still be considered active and that's Sony's ARccOS as f0dder mentioned).
I still use RipIt4Me if I need to
backup a DVD.
It's just a front end to DVDDecrypter but it was the first to actually scan through the structure of a DVD and modify the command structure to make the DVD jump to the first menu upon insertion into a player, (so you missed all the "forced" advertising). It also mapped out what 'cells' weren't used, or were small and bypassed those, (eg. FBI warning, etc).
Sadly, not developed any more, (it was Australian and got stomped on by Sony IIRC), but I've yet to find something it won't backup. The website was taken taken down but you can still find it out in the wild using a search.