MythTV

An all-in-one multimedia suite. MythTV works like a PVR (live TV, recording, commercial skip, etc), but also plays movies, music, photo slide-shows, etc. Excellent software, I use it extensively.

Players

mplayer

Plays many formats. Also has a related encoder (mencoder) for recoding video.

Amarok

Music jukebox

Exaile

Similar to Amarok. (nyt)

Totem

A multimedia player.

Xine

A multimedia player.

Editoring / Authoring

DeVeDe

For burning video DVDs. (nyt)

Items marked with (nyt) indicate I have not yet tested it. I've heard
it's good (so it has made it on the list) but have not yet tested it
myself.