DVDs are read by a laser, so they never wear out from being played since nothing touches the disc. Pressed discs (the kind that movies come on) will probably last longer than you will, anywhere from 50 to 300 years.
Expected longevity of dye-based DVD-R and DVD+R discs is anywhere from 20 to 250 years, about as long as CD-R discs. Some dye formulations (such as phthalocyanine and azo) are more stable and are expected to last longer, 100 years or more, compared to 20 or 30 years for less stable dyes. The phase-change erasable formats (DVD-RAM, DVD-RW, and DVD+RW) have an expected lifetime of 25 to 100 years.
In actuality DVDs often don’t last as long as the above statistically-based longevity figures would lead you to expect. Longevity can be reduced by problems in manufacturing or recording and by poor quality material. Shoddy pressed DVDs may deteriorate within a few years and cheap recordable DVDs may produce errors when recording or may become unreadable after a while.