Yes, DVDs still play on Blu-ray players, as well as Compact Discs (Music CD). I have also found that some of the cheaper Blu-ray and DVD players (Magnavox, Coby, etc.) will also play video CDs (VCD) and just about any type of disc I throw at them, while the more expensive players (Sony, Samsung, etc.) are very finicky about what they can play back.
Blu-ray players also "upconvert" your DVD to HD, and make your old DVDs look better. Not true HD, mind you, but they do look better.