You can use the same shoes for several kinds of exercises, but if you are serious about a particular sport, having the specific shoes for your sport specific workouts can be the difference between getting in shape and getting injured.
When considering shoes, consider the activity. If you are inside on a basketball or tennis court look for "court shoes" with stability--you don't need or want the tread and flexibility of a running shoe. If you get serious about cycling, invest in a pair of stable, lightweight biking shoes. In addition, you will need specialty shoes for boxing and mixed martial arts if you are serious about these activities. And choosing the right shoes is especially important for running. Don't run in walking shoes, basketball shoes, tennis shoes or cycling shoes. You will only end up with blisters at best and potentially more serious foot and leg problems.
When choosing any shoes, but especially running shoes, it's important to know some facts about your feet. Most people's feet fall into one of three categories:

• Flat feet: If you have flat feet, you need a shoe with more stability
• Normal arch: If your arch is neither too high nor too low, try shoes in both the cushioning and stability categories to determine which type suits your feet.
• High arch: If you have high arches you will need a more cushioned running shoe.

For specific foot issues, such as bunions, hammertoes or an ongoing injury such as plantar fasciitis, consult a podiatrist before shopping for sports specific shoes. The podiatrist can make customized orthotics to wear in your athletic shoes that will correct certain types of foot problems and prevent more.