Blu-ray won the format war.
HD DVD players were the first one to reach the market in April of 2006 and captured the initial market share. However. Blu-ray has prevailed. Although HD DVD lost the format primacy a small amount of titles is still being released on HD DVD in early 2008. The amount of new releases is likely going to dwindle in the near future.
Blu-ray is capable of higher storage (100GB on quad layer discs) which is an important factor when it comes to HD size picture.
While a consumer browsing the menus of the same title on Blue-ray and HD DVD may not see any noticeable difference, the underlining architecture is very different between the two formats. This inherent difference makes it impossible to author a disc for both formats in a single process.
Alternate DVD formats created specifically for HD are VCD HD, HD VMD, EVD, FVD. None of these formats are significant competitors in the United States.