I’ve found that the content that really shows off the HDTV format is that of the natural world. While sitcoms might be a bit more clear, the format really shines in situations where the extra detail is actually relevant, like in documentaries such as Planet Earth.
Here’s some of the best free high-definition content I’ve found on the web, if you know of any more please let me know!
Gravitas is a project by John Dubinski of the Department of Astronomy & Astrophysics at the University of Toronto. He works on visualization of galaxy dynamics, and his goal is to “use supercomputer simulations of realistic model galaxies to illustrate these slow and majestic dynamical processes on an accessible timescale and so breathe life into the iconic images of galaxies created by the world’s great telescopes”. He succeeds brilliantly, and has produced a set of captivating animations, some in HD.
Eric Bigas has a great website with several fractal animations, including a few in HD.
Hubble Space Telescope
The European Homepage for the NASA/ESA Hubble Space Telescope has tons of great HD content. Dr. Joe Liske at the European Organization for Astronomical Research in the Southern Hemisphere hosts a video podcast which you can subscribe to in 720p or full HD 1080p. They also have a HD video archive of broadcast quality footage, like this flythrough of the Hubble Ultra Deep Field.