Blue Ray & HD DVD discs

Does anyone know if Blue Ray and/or HD DVD video discs will play in a standard DVD player? I noticed my local video rental store is offering more and more of these and depending what is out, I may want to rent one of these to get the particular movie or video next on my list.

If they do play, would there by any pluses in video quality or would it be about the same as a standard DVD? I have absolutely no intentions of going to either format in the foreseeable future. Does anyone care to speculate if they believe that eventually DVD's will be available only in these two new formats?