And from almost there:
I kind of like classical music if it is slow paced and without singing, otherwise none is better.
If I listen to music, then it's mostly classics like sonatas by Bach, Beethoven, Chopin or Mozart. And it's always music that I know very well, so that it doesn't draw away my attention. For the same reason it's mostly music with very few instruments. You can't concentrate on coding and a fully orchestrated symphony the same time.
Jazz is another option. Again: Shouldn't be too complex. More like solo instrument. Keith Jarret playing piano is a good example.
Less likely other modern music. Singing I experience as distracting. Unless I don't know the language, so that I'm not tempted to follow it, Jan Garbarek playing sax together with the Hilliard Ensemble singing in Latin works great.
Though I listen to a lot of different music when I'm not coding.
None - I can't code while music is on. Ditto conversation, and ditto doing math.
There was something in PeopleWare (I think) about an experiment done with people listening to music. Those listening to their preferred music performed about as well as those who preferred silence and got it, and about as well as those who preferred music, but had silence. The group that preferred silence but had music performed, unsurprisingly, comparatively badly.
The sting in the tail was this. The task they were given had an "Aha!" insight buried in it. Namely, the full set of transforms they'd been asked to implement turned out to be trivial, although the individual components weren't.
All the programmers who had the "Aha!" moment had silence, regardless of their preference. No one with music saw the short cut.
I've since tried to find concrete evidence to support this anecdote, either papers, or first hand accounts, but the recounting in PeopleWare remains the only reference I have.
The reasoning behind this claim was that music "occupies" your right brain leaving only your left brain working on the task.
I don't know the validity of this claim as I haven't seen any academic studies backing it up.
In noisy situations I listen to ambient music. This is, frankly, not music I listen to at any other time, but it serves its design purpose of filling the sonic space without overly engaging my attention.
When I need a bit of noise I usually hit SomaFM. They have lots of great stations for coding, I recommend Mission Control, Drone Zone or Space Station Soma.