Yes, you can. The technology is called "ripping", and is of sadly dubious legality -- a lot of people use it to pirate movies for uploading. And yet, it's as much Fair Use as making a copy of a video tape for safekeeping, or of converting CDs to MP3s.
As Shira mentioned, DVDs usually hold 4 gigs or so of data. What Rippers tend to do is to re-process the movie to compress it down, in a manner again similar to converting CDs to MP3s. You'll lose quality, but not by much, and you'll save tons of space.
Sadly, the process is pretty complex, even for techies like me;
this article is a good start, and I actually use the Handbrake app mentioned there to watch my dance DVDs on my Palm TX. There's also any number of commercial apps that do this, but I know so little about them that I can't recommend one, even on hearsay.
Does that help any?