Worm gears are used when huge 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 established has: the worm can certainly turn the gear, however the gear cannot turn the worm. This is because the position on the worm is indeed shallow that when the apparatus tries to spin it, the planetary gearbox friction between the equipment and the worm holds the worm set up.
This feature is useful for machines such as conveyor systems, where the locking 
feature can become a brake for the conveyor when the motor is not turning. An added very interesting usage of worm gears is definitely in the Torsen differential, which can be used on some high-performance vehicles.