Can you play regular DVD’s on a an HDDVD player?
Or does it only make sense to buy one if you are buying the specially formatted DVDs?
Yes. And it's supposed to make them look better.
Regular DVDs will play in any HD DVD player, while HD DVDs will NOT play in a standard DVD player - so you have the option of buying regular or HD DVDs, with the bonus that the regular DVDs will be upscaled and look even better than they do in a regular player.
They do play "regular" DVDs, and upconvert them to make them look better on today's HDTVs. However, they will not play the competing HD format-Blu-Ray.
If I bought one, it would be so that I could play HD DVDs. If all you want is for your regular DVDs to look better, you can get a good upconverting DVD player for under $100. However, do not get a HD DVD player, or Blu-Ray player, or upconverting player unless you have a HDTV with an HDMI interface.