No. The groves where the data is stored on a blu-ray disc are much smaller than those of a DVD, which is one of the reasons it can store more data. A regular DVD player uses a red laser, whereas a blu-ray player uses a blue laser. Blue has a smaller wave than red, so it can read the smaller groves in the disc. On top of this basic difference in technology and physics, they're utterly different formats.
In summation: A DVD player cannot play blu-ray discs, but a blu-ray player can play DVDs
No you will need a Blu-ray player in order to play Bluray discs.
However a blu-ray player can play DVD's as well, so you are safe keeping your old DVD collection. The Blu-ray player will also upscale the DVD's to HD which is also a plus
Don't forget you need and HDTV in order to see the full potential of blu-ray so i recommend if you are thinking of purchasing a blu-ray player also purchase a new HDTV along with it.