Open Embedded Linux Entertainment Center (OpenELEC) is a small Linux based Just Enough Operating System (JeOS) built from scratch as a platform to turn your computer into a Kodi (previously XBMC) media center.Discontinued
Since 2017 source: https://en.wikipedia.org/wiki/OpenELECalso, the website is dead.
OSMC (Open Source Media Center) is a free and open source media player based on Linux and founded in 2014 that lets you play back media from your local network, attached storage and the Internet. OSMC is the leading media center in terms of feature set and community and is based...
XBian is a small, fast and lightweight media centre distribution for the Raspberry Pi, CuBox-i, Hummingboard and many more devices to come. It is based on a minimal Debian and therefore offers much of the same freedom as Debian offers.
MythTV is a free, open source media center and digital video recorder (DVR) distributed under the terms of the GNU GPL. With its plugin architecture, MythTV can be transformed into a home media center suite, capable of managing your personal photo, video, and music collections...
Easy-Data Mediacenter is a video and audio player with lots of tools. It is able to deliver bit perfect audio, and does not require any external codecs. It is able to run from a memorystick and does not require installation.