I know almost no one in their mid twenties or younger who doesn't. The, unsolved, problem is that music worth listening to is few and far between.
http://www.amazon.com/Shepherds-Dog-Iron-Wine/dp/B000TQZ7O4/...
So yes, there's a lot of dreck out there, but I don't think it's fair to say that one has to search very hard for music "worth listening to".