So if you've played sins a while, you probably have heard most or all of the music tracks. For me, one in particular struck me as really moving (and a few other runners up). What are yours?
To find the names of the tracks, navigate to the Sound folder inside your main Sins folder (e.g. C:\Program Files\Stardock Games\Sins of a Solar Empire\Sound) and listen to the largest .ogg files. The really small files are just transitions and other doo-dads; the actual soundtrack files are between 1 - 4 MB each.
In the unlikely event that you don't have an Ogg/Vorbis decoder, get with the times, man! Grab VLC from http://videolan.org for starters.
My favorite track is "Trouble 5". Really captures the tension of a risky engagement. "Sad 2" is pretty good sometimes as well.