In Hamlet, why is the ghost dressed in armor?

In the media studies class that I teach, I teach students that almost nothing in television and movies happens by accident. Viewers are seeing and hearing things exactly the way that the writer and director intend. What is said, how it is said, where an actor is and moves to, and what that actor wears is all carefully crafted to send viewers a specific message. Shakespeare plays are no different. He crafted lines of dialogue intentionally, and stage actions are intentional on his part as well. What each actor wears was also something that Shakespeare would have thought about. Public speaking classes always stress that audiences always remember far more than what was said. They remember how things were said and other non-verbal communication items. Shakespeare wants the ghost in armor because it sends audiences specific messages. Having the ghost in armor sends audiences the message that the ghost is ready for a fight of some kind. Dickens did the same thing with Jacob Marley. He's in chains to show audiences that his living actions wear heavily on him in the afterlife. The second reason that Shakespeare puts the ghost in armor is for quick identification purposes. I'm sure that you know people that always wear something specific, and you can identify them a long way off because of that article of clothing. Shakespeare is doing the same thing. The King's armor is going to be very identifiable because he's the king. He needs to be immediately recognizable so that his orders are never questioned. In Act 1, the armor's uniqueness is even commented on.

MARCELLUS: Is it not like the King?
ORATIO: As thou art to thyself.Such was the very armour he had onWhen he the ambitious Norway combated.

By putting the ghost in that armor, Shakespeare has left no room for doubt about who the ghost is.

The true reason for the ghost of Hamlet's dead father being dressed in armor is not entirely clear.
On the one hand, the armor does serve as an indicator that ghost is, without a doubt, the dead King Hamlet. As Horatio says, "Such was the very armor he had on / When he the ambitious Norway combated" (1.1.73-74).
This little detail, that the armor was what the King wore when he fought Norway, could have foreshadowing implications: At the end of Hamlet, it is Fortinbras, the bold Prince of Norway, who conquers Denmark. The detail of King Hamlet's armor, therefore, might be an indication that King Claudius has been working for Norway throughout the play. It would explain why Denmark was so ill-prepared for Fortinbras's incursion and give new political motivation for King Claudius's usurpation of the throne.

Though the armor worn by King Hamlet's ghost is a small detail, it actually serves an important role in the play. First of all, the armor worn by King Hamlet's ghost signifies that the ghost is on a mission dealing with martial conflict and war; since the ghost essentially wants Hamlet to combat injustice and wrestle the kingdom of Denmark out of Claudius' clutches, this martial theme makes sense. Secondly, the armor is actually important for the practical purpose of identifying the ghost as King Hamlet. For instance, take a look at this exchange between Marcellus and Horatio after they see the ghost in Act 1, Scene 1:

MARCELLUS: Is it not like the King?
ORATIO: As thou art to thyself.Such was the very armour he had onWhen he the ambitious Norway combated. (71-4)

From this exchange, we learn that the ghost is indeed the ghost of King Hamlet, as the apparition is wearing the former king's armor. By dressing his specter in armor, Shakespeare immediately tells the audience that King Hamlet has died and is haunting Elsinore. As such, the ghost in Hamlet wears armor not only to signify his warlike mission, but also to signify that he is the ghost of the former king.