Seneca's Ghost Adapted to Shakespeare's Time

What Shakespeare and his contemporaries did to the convention of the Senecan ghost was to make it unconventional. The old prototype of ghost was replaced by a humanized model with a mythology of its own - not a ghost that came from the ancient underworld of Tartarus, but from a Christian context. This new model was a spook from an English church yard, and his function was to haunt. There is a recognizable discomfort that comes from the presence of the Elizabethan ghost; a quality of both evil and threat. While outdated by the Protestant Reformation, there is a lingering sense that ghosts are a manifestation of the recently departed. They are dead, but not dead. This paradox is apparent in Hamlet when the ghost claims to be "doomed for a certain time to walk the night." Since the Protestant cosmology doesn't provide for an intermediate place between life and death (as the Catholics do), one wonders what a Catholic ghost is doing in a decidedly Protestant play. Regardless of these issues, which are played out in Hamlet, there is no question that this ghost is designed to be spooky. Both Marcellus and Horatio underline the dramatic terror the apparition evokes with images of the walking dead, unwholesome night, planets in rebellion, witches powers and charms, and the absence of God's grace.

An excellent description of the process by which the Senecan ghost became anglicized appears in Charles Edward Whitmore's The Supernatural in Tragedy.

We have seen that the influence of Seneca brought the ghost onto the English stage, but that from the very outset the native interest in the supernatural made him a figure of much greater significance than his classical prototype. Even where he remains confined to the prologue (which he seldom is) his malign power is subsequently referred to; and in the majority of cases he has a real relation to the plot. The desire for revenge which appeared sporadically in the classical ghosts becomes the dominant trait of their English successors, to such a degree that we may fairly say that the developed revenge-ghost is the creation of the Elizabethan age.
  -- Charles Edward Whitmore, The Supernatural in Tragedy, Cambridge, Harvard University Press, 1915. p.233.

In effect, Shakespeare's ghosts do a good job of reflecting the fascination with ghosts that prevailed during his time. Rich in paradox, they are both terrifying and engaging.