Where there is sweat and motion, there is chafing. A sports bra can prevent chafing by reducing the rubbing. Some sports bras put the seams on the outside to prevent chafing. Two readers complained about the scratchy labels inside bras, which they remove. Going braless altogether is not an option unless you take steps to tape your nipples to prevent chafing and bleeding, a problem also encountered by male runners.
Many women require a well-constructed, underwire bra even when on the trail.
Light spandex tops are not enough. Which bra and style a woman chooses depends on which problems she needs to solve. The worst problem is among those of larger cup size trying to find a bra that supports and controls motion without too much constriction. One woman wrote that she gave up running because of the motion control problem. Comfort vs. appearance can be a real tradeoff.