Regular cycling shoes used for outdoor use can be used as indoor cycling shoes as well, though many road cyclists prefer to use a different shoe for indoor use; road shoes are difficult to walk in when not on the bike. If a road cyclist chooses to use indoor cycling shoes with a rubber sole similar to that of a mountain bike shoe, he or she will need to use different pedals when cycling indoors, since road cycling cleats are large enough that they cannot fit on mountain bike shoes. Many people choose to use their outdoor shoes to avoid such a scenario.
If you plan on taking a spin class at a local gym or fitness center, you should probably consider buying indoor cycling shoes that are more like mountain bike shoes. Mountain bike shoes feature a rigid sole that will prevent excess flexing during riding, which is a similar design to road shoes. Mountain bike shoes, however, feature a rubber sole similar to a hiking boot that allows the cyclist to walk around without slipping or falling. These make great indoor cycling shoes, especially at the gym, because you will be likely to walk around in them before and after you use the cycling machines. These shoes also give you the option of using flat pedals or clipless pedals, which are pedals designed to lock over a cleat mounted on the bottom of the shoe.
If you do not plan on using clipless pedals, any shoes will work for cycling, but not all shoes will make good indoor cycling shoes. The keys to a good pair of indoor cycling shoes are rigidity, light weight, and a securing system that avoids laces. Laces can get tangled around the pedal axle or other parts of the bike, potentially leading to damage to the shoe or injury to yourself. Look for a shoe that features hook and loop straps that can be tightened down quickly and easily, or a ratcheting system that can be adjusted easily as well.
Make sure the indoor cycling shoes you choose do not flex while you are riding. The more the shoe flexes, the more pedaling power will be lost to shoe flex rather than transferred to the pedals and drivetrain. A flexible shoe, such as a running shoe or cross training shoe, is also likely to tire your feet out more quickly, which means you may end up cutting your cycling session short.