Music for me is lyrics I can relate to. I listen depending on my mood: I'm a mood listener, which also means that sometimes I don't care about the lyrics at all, because the sound is so good. Sometimes when I listen to music I just tap into the inspiration and write, mostly poetry and since a little while ago short stories too. Songs I've played in the background while writing poetry are for example: Riverside by Agnes Obel, Sugarcane by Missy Higgins, Lonely Hands by Angus and Julia Stone and many many more.
Sometimes it's a word in the lyrics or the melody of the song - the mood that does it. My epic novel from when I was young (a King Arthur fantasyish story) was mostly written with Moonlight sonata and Für Elise in the background to set the mood for my scenes (it drove my mum crazy to hear them on repeat).
My first English short story ever uploaded was written with The last snowfall by Vienna Teng in the background. It wasn't as much the words as the melody that inspired me.
In general though I mostly listen to symphonic/gothic metal, singer/songwriter and probably like 95% with female vocals. It just something that clicks better for me when hearing a voice like for example Sharon den Adel, though I have during my years listened a lot to Lars Winnerbäck who has on more than one occasion put words to my feelings, my sorrows and heartbreak. Music heals and inspire me.