I recently bought a Panasonic PV-GS19 (which I love) and have been making a lot of movies starring my family and my new wife. As you can imagine I'd like these movies to last for years, so I've been burning them to DVD. How long should they stay good? Apparently it's a matter of technology and quality. As with other products, DVD manufacturers mass-produce a huge number of units, many of which come off the assembly line with defects. The near-perfect units are sold under expensive brand names, and the slightly defective units are sold more cheaply through side companies. A knowledgable friend recommended Taiyo Yuden DVD-R discs to me through SuperMediaStore, and I haven't had any problems with them yet... but it's only been a couple of months.
Update 060117:
Reader John V. passes on this additional article about recordable media quality.
I would worry less about physical deterioration of the medium, and more about changes in hardware and software.
Some day it will be as hard to find a device to plan a DVD as it currently is to find a player for an eight-track tape or vinyl record. And some day playing a DVD (assuming you can read it) may become as difficult as playing an old DOS game or reading word processing files from the eighties.
If data is important enough to keep, it's important enough to keep in many places and in many forms of storage.
Lots of kids at school learn this the hard way when they bring in their research paper or something on a floppy disk and then something happens to the floppy disk, making it unreadable. Of course they don't have a copy saved to their storage space at school or a copy on their home computer.. so they get to do it all over.
My main problem with DVD's is scratches. DVD's use an error-correction scheme that is very similar to what CD's use, but because the data is so much denser a scratch wipes out a lot more bits and the error-correction often can't keep up. I've been extremely disappointed at how poorly movies do over time. It's useless to get movies from the library for that very reason.
I suspect that the Blu-Ray format (and whatever the other one is called) will be even worse, again, due to the increase in data density. They will have to greatly increase the number of parity bits to data bits just to maintain the status quo.