Ok, I'm just jumping into this thread w/ only skimming thru the responses.
But if u mean "ripping" as in decrypting the CSS onto your HD, then no, it won't damage your drive. If you mean "ripping" as in encoding the video into another format through a program that can handle the encrypted files, then it'll more than likely damage your drive. The main reason: overheating.
Depending on ur processor, encoding usually takes VERY long. So if it takes ur computer like say 15-20 hours to do it, then ur drive is about as good as dead.
EDIT: ok, looks like I'm just repeating what people have said before so I'll add some new material. There have been programs in the past that read directly from DVD when encoding. An example that comes to mind is a hacked version of DVD2MPG. I used to use this back in the day for DVD->VCD backups. VCD sux now anyways =P. To get high quality backups, the best way is to go thru multi-staged (and complicated) steps. In such cases, ripping to HD is just about essential.