Are typical worms and worm gears self-locking?

Does anyone know if typical/common worms and worm gears self-locking (plastic or metal)? Are the self-locking ones specially designed (with specific angles) in order to be self-locking? By self-locking, I mean that the worm gear can't turn the worm but the worm can turn the worm gear. Are they considered "special" worm drives, and thus cost more to make (and thus, less commonly used)?