I don't have an HTPC, I do have an Xbox 360 that acts as a Media Center Extender which gets it's data from an ...
AMD X2 4200+
2GB RAM
4x 500GB HDs + multi-terabytes (around 400GB of music and around 2TB of movies, some HD) of data shared on the network stored on 2 separate Linux boxes.
It runs on Windows Home Server and serves all my video/music needs both on the TV and on various extenders at my place. All of this is wired since wireless can't push through data fast enough to show HD content.
No display. It doesn't need it.
Built in video. It doesn't need it. It just needs the codecs
Everything else is standard. If you already have an HDTV, all you really need is a Media Center PC with an extender + wired connection to enjoy all your HD media in it's full glory. Plus the new Xbox 360s have HDMI built in although you don't need it for HD playback. You can also get a 360 to VGA converter.