It may be awhile before feature length films in HD are downloadable from the Internet, however at Vuze.com, you can download or stream high definition movie trailers, hot new music videos, and Showtime episodes like Dexter, Weeds, the Tudors, and more.
Download the VUZE software, then search for a variety of HD content. You can watch a 30-sec low resolution preview to make sure its something you want or verify it's what you were searching for. Then stream it or download the file to your hard drive.
You can download the files as bit torrents, though VUZE also downloads a .mkv file. I found it easy enough to convert this to an mp4 file, which is playable from iTunes. I can watch these HD files directly on my computer or sync the files to Apple TV and view them on my reference AV system. It's possible to further compress these files for playback on the iPhone and other mobile media devices.
There are probably more standard definition files than HD files, however, I am sure with time HD content will increase. It's also limiting what you can find, though in the course of an hour, I downloaded several music videos (studio and live), checked out some new movie trailers, and found Michael Moore's recent movie, Slacker Uprising, which is only available online. All this downloading is completely free and unhindered by ads tacked onto the downloaded content, though that is probably why there is limited content available.
This is a site I will be watching to see how it evolves.