There are many different supernatural elements in the poetry of Coleridge. Some reflect Christian beliefs, some reflect folk traditions, and some are fantastic elements grounded in his use of opium, which produced hallucinations.
One of his poems with many dreamlike and supernatural elements is "Kubla Khan," a poem that takes the actual Mongolian historical figure Kublai Khan, grandson of Genghis Khan, and uses that as a starting point for imagining a vast and supernaturally beautiful and luxurious "pleasure dome." Many of the elements of the poem, such as the phrases "demon lover", "holy dread," "sacred river," and, most importantly, "a miracle of rare device," create a supernatural atmosphere. The poem draws connections among artistic creation, the transcendent, and the supernatural as all distinct from and superior to mundane reality.
"The Rime of the Ancient Mariner" also has many supernatural elements, most importantly the albatross, which figures as an omen and a bird of good luck. Eventually, the albatross also figures in the curse brought down by the "hellish" deed of killing the bird. Supernatural imagery abounds, including spirits, witch oil, and, most importantly, the nightmare ship. The figure of Geraldine in "Christabel" is also one of supernatural evil.
These supernatural elements serve to distinguish the poetic world from the real one and a poetic way of thinking and imagining from uninspired literalism. They also seek to infuse the poems with an atmosphere of mystery and the sense of a dream world.