It is, for the most part, not legal to copy DVDs -- but it depends on what the DVD is. Most DVDs today are copy-protected. This means that the movie you rent from Netflix can't be copied legally and in fact most will be impossible to copy due to protective digital mechanisms on the disc itself.
However, some DVDs are not copy protected. Certain DVDs that you purchase may not have copy protection, although most movie and game discs do today. If you have, for example, a DVD of your family photos that was created for you, that may not be copy-protected. Similarly, if you have made a video that was transferred to DVD, the DVD might not be copy protected. In most cases it is not legal to copy any commercial DVDs that you rent or buy.
If you have purchased the dvd and want to make a daily use copy and store your original for safe keeping, it is perfectly legal under the fair use doctrine, but you may not copy rental DVDs so you can keep a copy.
There are several devices on the market that allow a person to make DVD copies and/or to convert VCR tapes to a DVD. Beware, they only work (for example) for home movies that are not 'copy-protected'.
If you personally used a VHS movie camera to record a Wedding fifteen years ago, it can be copied to a DVD using one of these devices. If your intent is to copy a commercially produced VHS tape or DVD disc, the odds are 99.65% against you, no matter what their advertizing claims their device can do.
Most DVDs today are copy-protected. This means that the movie you rent from Netflix can't be copied legally and in fact most will be impossible to copy due to protective digital mechanisms on the disc itself.
It's not so much a problem of making a backup copy for your personal use, but the way the law is written, breaking the copy protection is a bigger offense.
And although not *entirely* legal to do so, there is software that will copy anything.
And I mean anything. I can't tell you what they are because the forum doesn't encourage busting copy protection, but Google is your friend.
Somebody who isn't me (SWIM) used to rent and copy DVDs for personal use. SWIM found out that while it can be done it just is not worth the time and energy. Plus SWIM said sometimes the discs do not play correctly. Buting a dual layer DVD and wasting a few in order to save a few dollars does not make sense. Plus you don't have the nice box with the graphics. SWIM mentioned that there are sites where you download box artwork and print it out for your own DVD box. There are also artists who modify the artwork or create their own box graphics so as to avoid copy-write issues. It is all just a waste of time and ink IMO. Buy the DVD. There are a lot of people who get their salary from DVD and music sales. People you never see but are behind the scenes making it all happen.
Unfortunately, it is not legal to make DVD Copies in the USA per the DMCA since it requires breaking the DVD encoding. I have started a petition to encourage the government to recognize Fair Use for this: