Wearing a quality shoe and the correct type for your workout and foot shape will help prevent injury from exercising. Good shoes can lessen the impact of your step and cushion the foot from heavy landings. In addition, sport or exercise-specific shoes can improve your performance, enabling, for example, quick direction changes.
Running shoes are for forward-backward movement, so the sole can be more flexible. Typically the shoes are lightweight. Depending on a person's tendency to pronate (roll inward) or supinate (roll outward), they may need to look at a structured sole versus a neutral sole. Some athletic shoe companies have arch supports built into the shoe that helps with this. Usually, mid to long-distance runners (aka people who run for longer periods of time) want a roomy toe box and a generous width. The most important design elements of a running shoe, though, are the ones that help to promote a correct gait and help absorb some of the impact with the ground, which is
what eventually leads to joint overuse and injury.
Any lateral movements (done in SPORTS, BOOT CAMP, ZUMBA, STEP, and HIIT Classes) usually require more ankle stability, so a more rigid shoe is ideal for these classes. Typically, this means the shoes will be a little heavier, but that support around the ankle is crucial for those side-to-side movements. Cross-training shoes work well for this but again, each person needs to assess comfort versus support. I have had foot and ankle issues, so I always choose a more rigid shoe with slightly higher sides around the ankle.
Most people also want the ability to accommodate prescriptive and over-the-counter orthotic inserts. They have to be able to remove the cushion inserts in order to use what their doctor prescribed them for Plantar Fasciitis, Posterior Tibial Tendonitis, etc. Some newer shoes have the cushion insert glued or sewn into the shoe.
If you're an avid spinner, it's a good idea to get indoor spinning shoes. Spinning shoes are obviously great to connect the feet to the bike in order to use the legs in the most efficient way possible. Spinning or cycling shoes allow you to get a smoother pedal stroke and keep your feet in position on the pedal so you don't have to worry about your foot moving forward or backward. Unlike running shoes the soles of cycling shoes are stiff. The stiffer the sole the better the power transfer you get when pedalling and the faster you'll be able to go. The stiffer sole also means you will feel more comfortable and have better balance when you are standing out of the saddle.
You have dress shoes for work, sandals to wear to the beach, different shoes for different events in your life, so it makes sense to get a different type of shoe for whatever physical activity you'll be performing. If you're not sure what brand to utilize do some online research, if you have foot issues, talk to your podiatrist. Runners typically love BROOKS and I use Asics and New Balance shoes for more structured support. The type of brand you use is totally your preference, but make sure you are using a shoe that will support you no matter what the exercise!