Worm gears are used when large equipment reductions are needed. It is common for worm gears to have got reductions of 20:1, and also up to 300:1 or greater.
Many worm gears have an Reciprocating Vacuum Pump interesting property that no other gear arranged has: the worm can simply turn the gear, but the gear cannot turn the worm. That is because the position on the worm is so shallow that when the gear tries to spin it, the friction between the equipment and the worm retains 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. An added very interesting utilization of worm gears is definitely in the Torsen differential, which is used on some high-performance vehicles.