While there are many athletic shoes out there it is a good idea to use tennis shoes for playing tennis. This is important to reduce risk of injury and enhance performance. In fact there are shoes designed for different surfaces tennis is played on that are better suited for that surface - grass, clay, carpet, and hard court. Running shoes for example are good for forward motion, but tennis involves dynamic movements in all directions including a lot of lateral movement. Tennis shoes are designed taking this into consideration. The sole plays an important part for playing on different surfaces. Some good shoe tread patterns for different surfaces are - smooth sole pattern for carpet, herringbone pattern for clay court, dimples for grass and a combination of herringbone and dimple pattern for hard courts. So for example, the sole for playing on carpet wouldn't be a good option for clay courts. These days many shoe manufacturers sell all court shoes and these should be good enough for most players to play on different surfaces.