It's a terrible, terrible, terrible, terrible, terrible question. And a necessary one.
Why necessary? Hell, we need some way to talk about the stuff. And it's terrible, obviously, because there's no successful way to answer it. You're always leaving something out or implying something unthinkable. (If I include “mainstream pop” in my answer, aiming to lasso in someone as commercial as Lady Gaga, will you think I mean Ke$ha?)
Yet there are some exceptionally awful ways to describe your taste in music. One of them is, of course, to describe exceptionally awful taste in music. But this at least usefully indicates to the one listening that music is not going to be a fruitful topic in the current conversation. Plenty of common responses don't mean anything — or at least don't mean what they aim to mean. So here: the 10 worst answers to the question, “what kind of music do you listen to? (And yes, we've given some of these answers ourselves, more times than we care to recall.)
1. “All kinds of music.” (Also, “I listen to everything.” Frequently amended by, “Except country.”)
These common replies are never correct. If you literally think you listen to everything, you are ignorant of the amount of music there is. If you mean (as many people do) that you listen to both mainstream rap and modern rock, you owe it to yourself to explore some other genres. If you mean that you grew up listening to classic rock, got into punk in college, can get behind some hip-hop, chill out to Afropop, dig jazz, study Latin dance, savor going to the opera, and have a soft spot for gritty, old-school country, relax. This question just sucks.
2. “Whatever's on the radio”
A very bad sign. Nothing's wrong with the radio, but people who say this generally don't mean that they listen to radio stations that reflect their taste in music. They mean that they only bother listening to whatever combination of Top 40 shit-pop the commercial music industry has decided to foist upon them this week. (Obvious exceptions granted to Internet radio and to services like Pandora, whose users ought to appreciate the value of specificity in describing one's taste in music.)