I've actually thought about this a lot, and it seems to me that it would depend on whether you are referring to a more cinematic scene, or a song that represents the ship in your mind.
For my primary ship on my main character I have had a song that represents the ship to me for a long time. Its the U.S.S. Legacy, an Ops Odyssey class cruiser and it's song is an old track by Jethro Tull that was adapted from an old Saxon war dirge about Viking raids.
I don't really pick songs to go along with individual ships, but I do like to listen to Spotify playlists while I'm in-game. When playing storyline missions, I like to feel rather Trek-like, so I listen to this great Star Trek soundtrack compliation put together by TacPaddy. It's got music from virtually every series and movie and definitely puts me in the right frame of mind for storyline stuff.
However, when I'm doing STF's or causing mass destruction in the various battlezones, I want something more aggressive. I put together this playlist of pretty hard and fast metal and rock songs that gets me in the mood to blast my way through Borg, Undine, Voth, Vaadwaur, and anyone else who gets on the wrong side of my weapons.