Here's my setup:

Processor - AMD Athlon 64 X2 5600+ Windsor @ 2.8GHz ($139.99 on Newegg)
TV Tuner - HauppaugeWinTV-PVR 500 ($139.99 on Newegg). 2 Tuners so my girlfriend can watch Grey's while I record The Office even though they are in the same time slot. You could also add another card and have 4 tuners, although I'm not sure what the limit on Windows Media Center is.
Optical Drive - LG GGC-H20L Blu-Ray/HD-DVD/DVD/CD Drive. Don't care to bother with the format war? This drive is only $299.99 on Newegg and can play back both formats.
Video Card - ATI Radeon HD 2600XT ($114.99 on Newegg). This card offers full hardware offloading for VC-1 and H.264 (aka the Codecs HD-DVD and Blu-Ray use to compress their movies) so you won't kill your processor trying to play back HD content. Although the card has a DVI output, it comes with a DVI->HDMI adapter that will allow you to send sound out through the video card to the HDMI port of your TV or receiver. The sound is only 5.1, so those of your looking for the ultimate experience will still want to get a third-party audio card capable of doing DTS-HD or TrueHD. It is also HDCP compliant.
HD-DVD/Blu-Ray Playback Software - Cyberlink PowerDVD Ultra ($99.95) with AnyDVD HD (79 euros, $116.19 at the current exchange rate). I've heard that some people have had problems with this software, but I personally have not. It allows hardware acceleration with my graphics card and plays back smoothly. I don't typically use the extra features on the discs so I can't speak for its Web Content and other advanced functionality. AnyDVD HD comes in handy mostly when one component in your system isn't HDCP compliant. It removes the encryption from HD-DVD and Blu-Ray titles on the fly so you don't need HDCP to play them back. This also allows you to rip them to your hard drive and play them back on any computer which also has PowerDVD Ultra and AnyDVD HD. While my setup is HDCP compliant I still sometimes find it difficult to playback HD-DVD and Blu-ray titles without it turned on, but I'm yet to find out why.
OS - Windows Vista Home Premium ($109.99 for System Builder's License on Newegg)
Memory - 2GB PC2 6400 (price varies)
Hard Drive Space - 1TB (price varies). Storage is a huge part of any HTPC, especially if you want to digitize your entire movie collection. If I were to build a new setup today (and I could afford it) I would set up a file server or a NAS to store all of this. Attach it to a gigabit network and share all of it and you've got a completely disconnected place to store all your media.

Then don't forget your motherboard, case and power supply and you're good to go.

I saw somebody ask the pros/cons of the various cable connections, here's what I can think of

VGA - Pros - Higher resolutions than DVI in some cases
Cons - tends to crush colors, doesn't provide very good color range without customization. Some TVs don't have this connection. Analog signal, so it can be interfered with.
DVI - Pros - All digital signal to eliminate interference.
Cons - Many newer TV models lack a straight DVI connector. Too many connector variations (DVI-I, DVI-D etc.). Effectively obsoleted by HDMI.
Component - Pros - Cheap cables, good image quality for an analog signal. It is currently the standard analog medium for HD content.
Cons - Open to interference. Not many video cards offer Component out.
HDMI - Pros - Digital audio and video on the same cable, so no interference.
Cons - HDMI receivers are still expensive and so are the cables. HDMI versions can be confusing.

Well I've been with HD-DVD since the beginning (mostly because I despise Sony) and own about 20 or so HD-DVDs now. Another Engadget story earlier shows each major studio's stake in the formats (http://www.macrumors.com/2008/01/04/hd-dvd-vs-blu-ray-battle-over-warner-switches-to-blu-ray/) and if Universal and Paramount go, only Weinstien and Focus Films are left in the HD-DVD camp (at least with studios currently releasing HD movies on either format). This would effectively destroy any studio support that exists for HD-DVD and make it go the way of Betamax. If this does indeed happen, I hope hardware manufacturers do the right thing and release drives with dual-format capabilities so as to not leave anyone out in the cold (even if HD-DVD movies aren't in production anymore). Someone please correct me if I'm wrong but isn't the difference between the two formats as far as 0s and 1s are concerned simply in the way the data is stored on the medium? They both use the same blue laser so why can't manufacturers just develop HD-DVD "backwards"-compatible firmware to support the existing HD-DVD films if Blu-Ray is indeed victorious?

good luck to me!

Good luck to me.

Just so you guys know, all I had to do was plug my Xbox 360 HD-DVD player into my Vista Home Premium HTPC and it installed the drivers right away. My video card and TV are HDCP compliant so I have no worries there. Anyone without HDCP can just get AnyDVD HD and watch HD-DVD anywhere.