Nero and DVD Shrink. Nero will cost a little money ($5 + shipping). I got a copy at:
http://search.store.yahoo.com/cgi-bin/nsearch?catalog=5dollarsoftware&query=Nero&.autodone=http%3A%2F%2Fshop.store.yahoo.com%2F5dollarsoftware%2Fnsearch.html&submit.x=5&submit.y=8
Inexpensive and a great program.
DVDShrink is a freeware program that can remove the protection on a DVD and replace it after it makes a copy.
http://www.afterdawn.com/software/video_software/dvd_rippers/dvd_shrink.cfm
You will need to save the movie to your computer and then burn it with the Nero. Once you have completed making the copy you can delete the movie file from your computer as they do take up a lot of memory.
These programs work in concert very well and I've had no problems using them.
Also- I would recommend storing your DVD's in plastic cases rather than one of those 'book type' DVD/CD cases with the plastic pockets. I've found some of my CDs and DVDs have gotten scratched from using them. Stores like Kmart and Walmart sell plastic cases (the slim ones) that you can put CDs & DVDs in. They are relatively cheap (50 cases for $15-$20) and they protect the discs far better. I think because of the amount of motion that the soft cases (with the pockets) have- they tend to rub the CD/DVDs when you carry them or turn the pages.
Have a great day and hope this helps!!!