Worm gears are used when large gear reductions are needed. It is common for worm gears to have got reductions of 20:1, and also up to 300:1 or timing pulley greater.
Many worm gears have a fascinating property that no additional gear established has: the worm can certainly 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 gear and the worm holds the worm in place.
This feature is useful for machines such as conveyor systems, in which 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 normally in the Torsen differential, which 
is utilized on some high-performance cars and trucks.