Worm gears are used when huge gear reductions are needed. It is common for worm gears to have reductions of 20:1, and also up to 300:1 or greater.
Many worm gears have an interesting property that no additional gear established has: the worm can easily turn the gear, but the gear cannot turn the worm. That is because the angle on the worm is indeed shallow that when the apparatus attempts to spin it, the friction between your gear and the worm holds the worm in place.
This feature pays to for machines such as conveyor systems, in which the V Belt Pulley locking feature can become a brake for the conveyor when the motor isn’t turning. An added very interesting utilization of worm gears is normally in the 
Torsen differential, which is used on some high-performance cars and trucks.