What Shakespeare plays use supernatural references?
As the previous posts have noted, many of Shakespeare's works utilize supernatural references. Ranging from Julius Caesar's line, "The fault is not in our stars," to the storm that shipwrecks Prospero and the use of Prosper's magic, as well as "star crossed lovers" with regards to Romeo and Juliet, Shakespeare did not hesitate to invoke the supernatural to help enhance his themes and ideas. I would say that the two strongest uses of the supernatural would be the witches in Macbeth and the use of Hamlet's dead father in Hamlet. In the case of the former, the presence of the witches is not merely for dramatic effect. As Macbeth descends into a world of immorality, he comes to rely on the witches as a supernatural force that is almost guiding his hand towards his actions. Many thinkers, including posts here on enotes, have debated as to whether or not the witches themselves bear culpability for Macbeth's fate. The use of the dead father's spirit in the opening of Hamlet helps to establish this other worldly quality to the play, highlighting the moral quagmire that grips Hamlet in his relationship to other characters in the play. The use of the supernatural in this instance is to help create a situation to show the gulf between what should be and what is, a chasm excacerbated by the actions of individuals in the play.
Shakespeare has made a plenty use of supernatural elements, be it the sea-storm in the Tempest, the diety of Diana in Perciles, Prince Of Tyre, the ghost of King Hamlet in Hamlet, the King of fairies in A Midsummer Night's Dream , the three witches In Macbeth, ghosts of Posthumus's parents In Cymbeline and so forth.
The supernatural elements as one can discern, drive the plot ahead or bring in a major twist in the story. The most interesting thing to observe is the tact of Shakespeare in using such elements with an authenticity which compells us to beleive them as real or existing.