There are many varieties of Home Theater PC (HTPC) programs that work on Linux including MythTV, XBMC, Elisa, Boxee, LinuxMCE, Freevo and even SageTV. Even with all of those options, by far the most popular Linux HTPC program over the past years has been MythTV. Now I have zero experience with MythTV and very limited experience with Linux. If you're intrigued by the thought of HTPCs on a Linux computer, you definitely should check out the "MythTV vs. SageTV Smackdown" series at MissingRemote.
John Cabaugh, a long-time Linux user chronicles his experiences of both MythTV and SageTV and provides a very detatiled run-down of the pros and cons of each - all from a Linux user and HTPC user perspective. I'm not a linux user, but found the articles extremely interesting.
Missing Remote's MythTV vs. SageTV Smackdown - Part I