Check the Disc/Program
The first step you should take to make your DVD drive recognize your media is to check the media you're using. Often times, the DVD drive will fail in reading a DVD movie, CD, or DVD/CD-ROM based on the disc itself. Discs can get dirty or scratched, even when in their protective cases.
Before you get frustrated enough to start kicking things (namely your computer), pop out the disc and clean the outside. If possible, use DVD or CD cleaning products, as they are made to clean up discs with a special formula. Also, make sure to use a soft cloth to clean the disc; eyeglass cloths are a best bet or anything that is made to clean an LCD monitor. Don't use paper towels or towels or even your shirt. Abrasive cloths actually make any imperfections worse, as they can also cause scratches.
Next, if you use a certain program to watch DVD movies, like Power DVD or Win DVD, check to make sure the program itself is working. Go to the program website and see if there is an update. It's always best to keep up with updates, as new features or fixes are involved that make movie watching better than before.