Where do we see supernatural forces having an impact in Hamlet?
The most important supernatural force in the play is the figure of the ghost. The ghost appears at the very beginning of the play to add mystery and suspense to the action. In fact, the entire first act of the play is almost entirely devoted to discovering the identity and purpose of the ghost's appearance. Horatio even connects the supernatural events occurring around the ghost's appearance to those events that supposedly occurred at the death of Julius Caesar.
Once the ghost claims to be the murdered father of young Hamlet,the supernatural continues with the ghost's command to Horatio and Marcellus to "SWEAR" they will keep the identity of the ghost a secret. The rest of the play revolves around Hamlet's dealings with the ghost's accusations against Claudius. Hamlet must first prove to himself that the ghost is telling the truth. He does this through the performance of "The Murder of Gonzago". The ghost then reappears as Hamlet is rebuking his mother for marrying his uncle. This scene adds to Gertrude's belief that her son is indeed mad. However, she agrees to keep Hamlet's secret.
Even though the ghost does not appear again, the events that occur are all consequences of his accusations and demand for revenge. Thus the entire motivation for the play would be absent were it not for the supernatural appearance of the ghost.