Worm gears are used when large equipment reductions are needed. It is common for worm gears to have got reductions of 20:1, and actually up to 300:1 or greater.
Many worm gears have a fascinating property that no other gear arranged has: the worm can simply turn the gear, however the gear cannot turn the worm. That is because the angle on the worm is so shallow that when the gear tries 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, where the locking feature can act as a brake for the conveyor when the motor is not turning. One other very interesting usage of worm gears is Planetary Gear box certainly in the Torsen differential, which is used 
on some high-performance vehicles.