YES! Sports bras are needed.
For one thing, when you do any exercise, if your shirt flies up, nobody will see anything!
For another, If you happen to be well-endowed, a sports bra is more supportive than a regular bra for athletic movement. Most of them are also designed to "breathe" so that you're not drenched in sweat.
Sports bras can be divided into three kinds: Low impact, Medium impact and High impact.
Low-impact sports bras with comfortable detailing provide light support for yoga, Pilates or barre workouts.
Extra support in medium-impact sports bras help elevate your performance for that next gym, spin or studio class.
High-impact sports bras offer maximum support with molded cups for high-energy runs and aerobics.