The VideoLAN Forums

Mac The Ripper, AnyDVD or which other DVD ripping app would most likely be the "safest" as well as being the easiest
to use? That is, I certainly wouldn’t want to use software causing any risk of damage to my original (copy-potected) DVD movie disc-such as making any of its features unplayable again in any standalone player or computer drive.

Do both of these apps have to "re-burn" the disc in order for the user to copy it?

These apps don't try to write onto the original disc but are either ripping unprotected files to the HDD or decrypt on the fly in the case of AnyDVD.
In either case there is no risk for the original DVD as long as long you don't try anything fancy and follow the software manual instructions.