Air motors generally do not overheat and cannot "burn out" and cause an explosion, so they are considered safer than electric motors, and they are much cheaper and smaller than explosion proof electric motors.
Dust and splashes of water cannot enter a pneumatic motor, so they are a better alternative than an electric motor in these situations. Stainless steel and sealed pneumatic motors are also readily available for under water use.
Air motors are much smaller and lighter than electric motors of equal specifications. This makes them perfect for hand held power tools, robot end or arm applications, as well as any applications where easy change over of the motor is necessary.
Pneumatic motors are not damaged by stalling, provided that their gearing can withstand the stall torque. Pneumatic motors can be stalled indefinitely and will start again as soon as the load is removed. Electric motors will overload and can burn out if they are stalled unless there is some kind of torque limiter or overload protection installed.
Air motors are easily reversed using air valves. They even can be reversed without waiting for the load to stop (providing the gearing can withstand the torque).
Air Motors achieve high torque at low speed naturally and repeatedly starting or stalling them under full load will not damage them, providing the gearing can withstand the torque.