Like most legal questions, it's difficult to pinpoint a yes or no answer. Let's look at a few of the laws / regulations / court decisions that come into play.
Fair Use - It worked for BetaMax. The case went to trial in 1979. In the blue corner: Universal and Disney and in the red corner: Sony. It was a knockout in the first round with the decision going something like this:
Handing down its decision in October 1979, the U.S. District Court ruled in favor of Sony, stating that taping off air for entertainment or time shifting constituted fair use; that copying an entire program also qualified as fair use; that set manufacturers could profit from the sale of VCRs; and that the plaintiffs did not prove that any of the above practices constituted economic harm to the motion picture industry.
See that part in the ruling about time shifting? That's why you can use that nifty DVR / Tivo to record all your favorite shows and fast forward through those pesky commercials. So it seems like fair use would allow us to make a backup copy for personal use dosen't it? Except......
The DMCA and 321 Studios: You remember 321 Studios right? They had that DVD copying software that many people were using 5ish years ago? Well they were taken to court and a ruling was made that goes something like this:
321 Studios v. Metro Goldwyn Mayer Studios, Inc. et al., that the making and selling of products that permit users to reproduce motion picture DVDs violates the Digital Millennium Copyright Act (“DMCA”). It is important to note that this case addresses the vicarious liability of manufacturers of copying products, rather than the fair use and other rights of purchasers of DVDs. Under the Copyright Act, legitimate owners of DVDs possess the right to make backup copies and other fair uses of their DVDs; manufacturers and sellers of products that assist these DVD owners in exercising their rights do not themselves possess such rights. Since suing home users is bad business, creators and sellers of copying and related products make safer defendants.
Digital Millennium Copyright Act
Sections 1201(a) and (b) of the DMCA prohibit the manufacture and distribution of devices that circumvent a technological measure meant to either control access to copyrighted works or to protect the rights of copyright owners. 17 USC 1201(a), 1201(b). However, these anti-circumvention provisions are qualified by the use rights of DVD owners in the remainder of the Copyright Act. See 17 USC 1201(c)(3).
The following is my opinion only. It seems like making a backup copy of a DVD for personal and archival use falls directly under fair use. It also seems like any software that circumvents CSS on a DVD is in violation of the DMCA. So, If you can make a backup copy of the DVD without violating the DMCA and breaking the CSS, it seems like that would be within the bounds of fair use and not in violation of the DMCA.
The reality is that as long as you are not selling or making copies available to anyone, you are probably in the clear either way. The companies like 321 Studios that make software to bypass CSS and other DVD encryption are the ones they will go after.
Some further reading on the DMCA.