Bra straps often to cause shoulder pain, neck stiffness, and back ache. Its almost always due to two things: large breasts, and poorly fitted bras.
Now before you run to the local plastic surgeon and ask for a breast reduction, there is a lot you can do to reduce the load. Firstly, make sure the bra is fitted correctly. Read my article for help on how breast size is determined, and how bras are fitted.
Secondly, maintain good posture.