When I write, I don't listen to music.
When I do listen to music, I want to sing along.
When I want to sing along, I want to sing along for a reason.
When there's a reason to sing along, a song has character.
Therefore (and we have some transitive property happening here), I like to listen to music with character. (And I don't listen while I write because I need to focus on my own characters.)
"Character" doesn't necessarily mean that the song literally is about (a) character(s) (though that usually works--see Roxanne by The Police and Eleanor Rigby by The Beatles). For me, a song with character has some sort of meaning--whether I am intrigued by a story being told (see Skullcrusher Mountain by Jonathan Coulton and The Downeaster "Alexa" by Billy Joel) or the song reminds me of a favorite TV show (see "every song ever used in Supernatural").
And when I like a song and its lyrics I like to learn them and sing along, whether out loud (see "when I'm alone/with my sister in the car") or in my head (see "every time other than the aforementioned two circumstances").
The same characteristics that I find intriguing about songs I also find intriguing about stories. Character. Meaning. So what does your favorite song say about your favorite book?