I've been traveling a lot recently, and rather than bring my expensive original DVDs with me, I've been looking at different ways of backing them up using my Mac, so I can view them on the road, but not have to worry about accidentally leaving them in the hotel room. After researching, I've come up with three ways that I use regularly, depending on how much time & effort I want to expend on the process.
MTR does an excellent job of ripping the DVD data to your hard drive, and in the process removing encryption and region code limitations. This is great if you have enough space on your PowerBook or iBook hard drive, as you can watch the ripped folder full of video with the Apple DVD Player, just like you would any other DVD, and at full quality. The only drawback being their site seems to be up and down like a roller coaster --- keep trying through, and you should eventually be able to download it. Of course, if you're not bringing a laptop, but only a portable DVD player, you'll want...
Popcorn does a very good job of taking your unencrypted DVD (or your decrypted folder from MTR, above), and recompressing it to fit on one burned DVD-R (or even a DVD-R-DL, if you're lucky enough to have a dual-layer drive and cheap enough blanks to make it worth the effort). It's not perfect--- especially if your original is a dual-layer high-quality disc, you'll notice the re-compression creates a much softer-looking video. But, heck, if you're only viewing it on a 7-inch screen anyway, it does a pretty decent job.
The third way is to use Handbrake on either your original disc or ripped folder, and let it create an MPEG-4 file of the video for you. It's not as high quality as either option 1 or 2, and takes a lot longer to compress, but it does end up a heck of a lot smaller, so you can end up fitting, say, a season's worth of a show on one DVD-R, if you crunch it hard enough. In addition to regular ol' MPEG-4, Handbrake also supports creation of AVC or H.264 videos, which give you a mighty decent looking picture for the data rate. Of course, you'll need either QuickTime 7 or VLC to view these.
Of course, don't forget that making anything other than personal-use-only backup copies of copyrighted DVDs that you own is a crime. But if you're looking for a way to protect your valuable discs while enjoying the content on the road, rip away!