What music do you listen to while reading?

I don't. I've tried having some background music while reading but it usually distracts me too much.

I generally don't listen to music while reading except on the rare occasion of a re-read or if I really don't care about something that I'm reading for a class (did this more than a few times during my Young Adult literature class last semester, I'm sorry Professor Reid!). If I haven't read something yet, I don't know the tone or what would fit. Worse, if I go for what I think would fit a book, I'm really supporting my own preconceived notions about it and it causes me to resist anything else that it tries to do.

But on the occasions that I reread, it's usually something I'm very familiar with and don't have to think about having on. Boards of Canada, Godspeed You! Black Emperor, Black Sabbath, DJ Shadow, J Dilla, Kraftwerk, etc. Not terribly exciting answers, I know, but that's the idea for me unless I want to curate a few albums to a specific book. I only want to listen to things that I've listened over and over so there isn't a single idea on there that can catch me off guard and take me out of the book.

If I just don't give a shit though I pick something that looks interesting off RYM and play it so reading doesn't feel like a total waste of time. I think I found Toundra and Stars of the Lid that way.

Music only distracts me

Lately I’ve been listening to ambient soundscapes like the ones you can find at ambient-mixer.com, although YouTube is also a good source for hours-long soundscape tracks. It demands less attention than podcasts and is less involved than music.

When I find time to read I really enjoy listening to music at the same time. That can be anything I listen to normally so not really suggestive, although the last few days I heard mainly Of Monsters and Men which I can recommend.

Hearing the music after I am finished with a book reminds me of the mood I was in when reading and 'transports' me back into the world for a bit which I very much enjoy.

I used to do this while taking the train to and from work, because apparently reading isn't enough of a sign that I don't want to talk to some random person about the lint they found in their navel that one time.
Crazy, I know!

In answer to the question, I just listened to anything I was into, Blink 182, The Offspring, Disturbed, Korn. all that sort of stuff

I can't do music and books unless it's an intentionally shallow book, but then mostly random: opera, country, old rock, jazz, soundtracks, Frank Zappa, shakahuchi, techno, R&B, choral, as broad as I can get it.