Worm gears are used when huge gear reductions are needed. It’s quite common for worm gears to have reductions of 20:1, and even up to 300:1 or greater.
Many worm gears have a fascinating property that no additional gear established has: the worm can simply turn the gear, however the gear planetary gearbox cannot turn the worm. This is because the position on the worm is indeed shallow that when the apparatus tries to spin it, the friction between the gear and the worm retains the worm in place.
This feature is useful for machines such as conveyor systems, in which the locking feature can become a brake for the conveyor when the motor isn’t turning. One other very interesting usage of worm gears is usually in the Torsen differential, which can be used on some high-performance vehicles.