Worm gears are used when huge gear Torque Arm 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 an interesting property that no other gear set has: the worm can easily turn the gear, however the gear cannot turn the worm. That is because the position on the worm is indeed shallow that when the apparatus tries to spin it, the friction between your gear and the worm keeps 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 isn’t turning. An added very interesting use of worm gears is normally in the Torsen differential, which can be used on some high-performance cars and trucks.