I usually answer that I like any music that answers to three requirements: a good singer, a good melody, and lyrics that have something to say, or are funny. That more or less automatically excludes all modern pop songs :) - No, I know, there are some exceptions.

If I come up with names like Tom Lehrer or Tom Paxton most people look rather blank: in my country, The Netherlands, they are virtually unknown.
I could also answer that I like Grieg or Chopin - liking classical music is quite an acceptable answer to the question, and most people do have a picture then...

Cheers, Ingrid