What kind of music do persons born in the 1940s in the United States like in 2009?

Everybody is different so you simply can not generalise as to what sort of music any individual will like or dislike by when they were born. Most people born in the forties are most likely to enjoy the kind of music they were brought up with, which in many cases will be pop hits that came out in the late fifties or early or mid sixties, particularly chart toppers of that epoch. Some will be very much into Jazz and some into Classical Music where people of that age group are most likely to enjoy music by Beethoven, Mozart or Hayden rather than music composed in the twentieth century, Generally people of that age group will not enjoy rock as much as people born in later years, nor are most likely to enjoy heavy metal, but there are plenty of exceptions.