If you have little kids, dogs, cats, hamsters, or clumsy adults in your household, you need DVDShrink. It allows you to rip the contents of a DVD (including copy protected DVDs) with essentially a single click. By default it creates a 4.3 gigabyte file, just right for burning to a backup disk. You can also just keep the files on your PC or laptop if you want convenient movies without lugging the DVDs around.

I really can't recommend this product strongly enough. It is free... unfortunately the original author had to stop supporting it due to pressure from the MPAA, but it isn't illegal to back up your DVDs no matter how much they may wish it was. If the download link I gave you goes away, try searching Google for dvdshrink32setup.zip.

If you're a linux user, I've seen K9Copy recommended. I haven't used it (I do run Ubuntu on my main desktop; I just haven't had time to try the app yet) but it looks nice from a superficial glance.