The “Audio Home Recording Act”, passed in 1992, contains this passage: “No action may be brought under this title alleging infringement of copyright based on the manufacture, importation, or distribution of a digital audio recording device, a digital audio recording medium, an analog recording device, or an analog recording medium, or based on the noncommercial use by a consumer of such a device or medium for making digital musical recordings or analog musical recordings.”
http://en.wikipedia.org/wiki/Audio_Home_Recording_Act#Exemption_from_Infringement_Actions

Basically, this means that if you’re making copies for a family member, or copies for use in a car, even though it’s still technically copyright infringement, the copyright holder can’t sue you or do anything about it.

Furthermore, the “fair use” doctrine under US copyright law states something similar:
“Notwithstanding the provisions of sections 106 and 106A, the fair use of a copyrighted work, including such use by reproduction in copies or phonorecords or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include—
the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
1. the nature of the copyrighted work;
2. the amount and substantiality of the portion used in relation 3. to the copyrighted work as a whole; and
4. the effect of the use upon the potential market for or value of the copyrighted work.”
There have been some court cases that imply that format-shifting (making MP3s of a CD you own, or making a CD of a DVD you own [as you're doing], or making a DVD of a VHS tape you own, etc.) is legal under these “fair use” provisions of copyright law. (See e.g. http://www.eff.org/IP/eff_fair_use_faq.php, #4).

That said, DVDs are in a murky area because of two things: encryption and the DMCA. DVDs are digitally encrypted, meaning that it’s impossible to copy them without “cracking” their code. Furthermore, the “Digital Millennium Copyright Act”, or DMCA, passed in 1998, “criminalizes the act of circumventing [encryption], even when there is no infringement of copyright itself”. (http://en.wikipedia.org/wiki/DMCA) This means that, even though you might be fully within fair use rights to make copies of your DVD, or format-shift into MP3s or a CD, the DMCA makes breaking the DVD’s encryption (which you must do in order to format-shift) illegal. This is hugely controversial, and the DMCA is widely regarded on the Internet as a bad law. Regardless, it is the law.

All that said, if this is all for personal use, you have exactly zero chance of ever being sued. There have been absolutely no court cases (as far as I am aware) that involved solely personal-use copyright infringement. All cases either involve widespread distribution (such as peer-to-peer filesharing) or some sort of commercial benefit. You basically have nothing to worry about from a legal standpoint, despite the technical illegality under the DMCA (due to DVD encryption).

The moral issue is a completely different kettle of fish. Let’s just say I personally believe that format-shifting is, and always will be (regardless of circumstance or legality) completely morally acceptable, and leave it at that.

Hope that helps!