Worm gears are used when huge gear reductions are needed. It’s quite 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, however the gear cannot turn the worm. This is because the angle on the worm is 
indeed shallow that when the apparatus attempts to spin it, the friction between the equipment and the worm holds the worm in place.
This feature pays to for machines such as conveyor systems, in which the planetary gearbox locking feature can become a brake for the conveyor when the motor is not turning. An added very interesting use of worm gears is certainly in the Torsen differential, which is utilized on some high-performance vehicles.