Worm gears are used when huge equipment reductions are needed. It is common for worm gears to have 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 simply turn the gear, however 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 your equipment and the worm keeps the worm set up.
This feature pays to for planetary gearbox machines such as for example 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 usually in the Torsen differential, which can be used on some high-performance vehicles.