I agree with Post #2, people were a lot more superstitious in Shakespeare's time day and age.  Ghosts and things that went 'bump in the night' were part of their popular culture. Even at a time when the church was extremely, extremely powerful, people still held onto their superstitious beliefs about fairies, witches, ghosts, changelings, sprites.

There was probably a more pervasive belief in some supernatural concepts in the Elizabethan period than we see now. They had their share of witchcraft trials, probably more than their share, and a natural tendency to ascribe unexplained events to superstitious causes. The general societal acceptance of the idea of supernatural activity probably made it easier for Shakespeare to include ghosts and witches in his work than it would be today.