Jason, you can read about the so-called CD rot here. DVD rot is much more rare, there are only a few pressed DVDs that were affected and those were some of the very early releases.
DVDR media is a lot more vulnerable to "rot" since organic dye is used for the recording layer. Symptoms are described on the above-mentioned pages. However you need not worry: as long as you buy quality media and keep in in cool, dry place (no, a refrigerator won't do =) away from sunlight, and the ambient air is not heavily polluted, your media should be fine.
Btw, movies don't come on CDs (except for the South/East-Asian markets where VCDs are popular). Those shiny round things are called DVDs.