Why not just ask that the person turn down the volume on their player? He/she probably doesn't know that you can hear the music. If that doesn't work, ask that a flight attendant help, if on a plane, or switch seats, if on some sort of public transportation.

You will need a willing accomplice for this one. Personal music players are supposed to be personal. Sometimes the excessive, tinny continual noise on long journeys can be very irrating so - strike up a pretend conversation with the other passenger and glance continously at the annoyer, occassionally pointing at them. Remember to laugh and smile all the time. The Annoyer will naturally assume you are discussing them so will turn the music down or off to hear your "conversation". At this point look sheepish and stop talking. If they increase the volume again, simply repeat the procedure. Used this ploy 3 times now and it really works.