Research suggests that when exercising, women should wear a good fitting sports bra, to reduce movement and pain, help prevent back and neck pain, and prevent stretching of the Cooper's ligaments which help to hold the breasts up.  Repetitive trauma to the breasts, running, bouncing etc., can stretch the Coopers ligaments permanently, unless supported properly with a good sport bra.

An Australian study tested a fashion bra, crop top and bare breast against a sport bra. The sport bra reduced pain and vertical movement by over 50%. It is not just the larger breasted woman who suffers pain when exercising - up to 56% of all women endure discomfort.

A good sport bra should have complete cups to prevent movement of the breasts in all directions. It should also have wide, non-elastic straps, and fastners should be covered to reduce rubbing against the skin. ‘Breast droop’ is irreversible so prevention is the best option.
(Australian Institute of Sport, Canberra, Australia. University of Portsmouth, England)