There are quite a few software programs that allow you to copy DVDs for free. Some of the more popular ones include DVD Shrink, ImgBurn, and Nero Burning Rom. Each program has its own set of features and capabilities, so it's really a matter of personal preference as to which one you choose.
DVD Shrink is perhaps the most well-known of the bunch, and it's definitely one of the easiest to use. Simply load your DVD into the program and hit the 'Start' button. It will then compress the video files on the disc so that they'll fit onto a blank DVD. The trade-off is that you won't be able to fit as much data onto the new disc, but it's still a quick and easy way to make a backup copy.
ImgBurn is another excellent choice for copying DVDs. It's a bit more versatile than DVD Shrink, offering support for different types of discs (including Blu-ray) and file formats. It also burns data at faster speeds, so if you're in a hurry, this might be the program for you.
Nero Burning Rom is probably the most feature-packed option on this list. In addition to being able to copy DVDs (and Blu-rays), it can also be used to create CD and even HD DVD discs. If you're looking for an all-in-one solution, Nero Burning Rom is definitely worth considering.