If we all ran like Bo Derek did in the movie "10" we would have some serious stretch marks right now.
Sports bras do prevent the painful bouncing, yes. But more importantly though they prevent permanent breast saggage, That's right — it's not just old age and gravity that will make your boobs hang low. High-impact activities, like running or even spinning, can stress your Cooper's ligaments (the connective tissue that keeps breasts firm), causing your breasts to sag more quickly.
Compression bras work best for smaller-busted women.
I like this one:
Bonus – this bra makes you look va va voom.
For the more well-endowed (D cup +) you should opt for an "encapsulation" bra that supports each breast separately. I've heard great things about this one:
It's best to replace workout bras every six months to a year. That way your bra will stay tight to your ta tas!