Worm gears are used when large equipment reductions are needed. It is common for worm gears to possess reductions of 20:1, and actually up to 300:1 or greater.
Many worm gears have a fascinating property that no additional gear set has: the worm can simply turn the gear, but the gear cannot turn the worm. This is because the angle on the worm is indeed shallow that when the gear tries to spin it, the friction between your equipment and the worm retains the worm in place.
This feature is useful for machines such 
as conveyor systems, in which the locking feature can become a brake for the conveyor when the motor is not turning. An added very interesting utilization of worm gears is planetary gearbox usually in the Torsen differential, which is used on some high-performance vehicles.