Some good answers and some dead wrong too.
Here's my take.
First question should be can you take advantage of HD? If you don't have a 1080p HDTV, preferably ~40" or more, and with an HDMI input you won't see much benefit from either HD format (relative to a good upscaling DVD player).
If your equipment 'qualifies' here are some considerations re choosing a format.
First, there is no noticable difference in video or audio quality from the two formats.
Second, the much touted higher storage and higher bitrate capacity of Blu-Ray vs HD DVD is irrelevent in the real world. All movies fit either format, and the effect of bitrate -- in an era of efficient audio compression and advanced psychacoustics -- is unimportant. In fact some lower bit rate sound tracks are BETTER than higher ... including "lossless" PCM.
The real difference is in hardware. The HD DVD format is a stable, mature format (current players are 3rd generation ... with each iteration being sleeker, higher performance and lower cost ... but all meeting the complete HD DVD spec), while Blu-Ray is a 'work in progress'. All existing Blu-Ray players fail to meet the recently adopted BD-Video (1.1) spec, and because so many of the features that are mandatory in the HD DVD spec are optional in the Blu-Ray world the movie studios don't know what to program for (one of the main reasons Blu-Ray disks are often released later than HD DVD versions or have fewer special features .. for example picture in picture and on-line extras (even the recent 1.1 Blu-Ray spec doesn't require a LAN (Internet) connection ... that isn't required until V2.0).
I could go on, but the conclusion is plain, Blu-Ray, from a hardware perspective is a mess ... and there is no hope of fixing it in new players until at least late this year, and more likely Q1 of 2008.
From a price perspective, the intro level (1080i) HD DVD is much cheaper than any of the Blu-Ray players (though to be fair, when comparing similar 1080p machines prices are much closer (although remember the earlier point about existing Blu-Ray players being crippled relative to all HD DVD models!)).
Now the big question ... will either format 'win'. The jury is out, although a conclusion is likely by the end of Q1 2008, since by that time Warner will probably decided which format to abandon (Dreamworks & Paramount abandoned Blu-Ray a couple of months ago), and that decision will decide the 'war'.
Currently HD DVD are on a bit of a roll, having sold 90,000 players over the US Thanksgiving weekend ... and that may translate into disk sales (or it may not). In Europe, 75% of stand alone players are HD DVD, while in the US it's about 60%. BUT, disk sales favour Blu-Ray.
However, given that only 14% of US households have an HDTV (the basic requirement to take advantage of either HD disk format), and only a portion of them can benefit from HD disks (Because many HDTVs don't have HDMI inputs, or are only 720p models, or are too small). So ... the current proportion of all disks sold (about 95% DVD and 5% HD DVD or Blu-Ray) is more or less a limit until 1080p HDTV penetration increases. And by then on-line HD downloads (facilitated by more efficient compression formats) may be a more viable option. After all, MP3s have demonstrated that convenience is more important to most people than quality (CD, SACD, DVD-A, etc), and the same could prove true for HD video.
The bottom line is that HD DVD and Blu-Ray, whether one 'wins' or not, is destined to be a niche format for some time to come.
Unless you really want to jump in now, I'd wait before buying. Prices can only come down, movie choice improve, and rental options expand (cf purchase of ridiculously high priced HD disks).
I personally have an HD DVD, but won't be buying very many disks since there are very few movies worth the price gouge for the small incremental quality improvement I get over DVDs on my 1080i projector and 110" screen using an Oppo upsampling DVD player.
Objective analysis suggests consumers are being herded by ads and hype to spend $$$ to buy into something that is crippled (HDCP, BD+, HDMI and other half baked or anti-consumer overhead) and of little real benefit.
If you do want to try HD disks for yourself, go for HD DVD ... it will cost you less, allow you to play HD DVD disks and give you a good upscaling DVD player to play the standard DVD version of kids pictures on (where most Blu-Ray disks aim) or as a player for your existing DVDs after the future becomes clearer.
Hope this helps.