Poltergeist, from the German words polter, meaning noise, and geist, meaning spirit, is a supposed kind of ghost that, as its name implies, allegedly causes unexplained noises such as banging on a wall, footsteps on a floor, slamming doors, even throwing things. Some have even allegedly pushed, struck or otherwise assaulted people. Reports of them have been made for centuries. While many, or most, can simply be explained by natural causes, mental illness of the "witness," honest misperception, or outright fraud, others have not been accounted for.
Do "Ghosts" Really Exist?
The Bible plainly states that the spirit world is teeming with life. God Himself of course is Spirit. The Holy Spirit of God (called the "Holy Ghost" in earlier translations of the Bible) is Spirit. God also created countless billions of angels, the good ones being the friends of Believers (e.g. "Are they not all ministering spirits sent forth to serve, for the sake of those who are to obtain salvation?" Hebrews 1:14), but there are also angels who rebelled and sinned, known now as demons (or "devils" in older translations). The chief among these is Satan himself who became a wicked rebel (see Born To Be Wild? and What Does Satan Look Like?)
But what are "ghosts"? Are they angels of some sort? Or are they spirits of humans who have died?
There is only one recorded incident in the Scriptures of the spirit of a dead human seeming to appear to someone, that of Samuel appearing to Saul. It's important to note that, if it was somehow actually the spirit of Samuel, as it seems to have been, the rare incident was to deliver a Godly message, not to scare or haunt anyone:
"The king said to her, "Have no fear; what do you see?"
"And the woman said to Saul, "I see a god [or a spirit NIV] coming up out of the earth."
"He said to her, "What is his appearance?"
"And she said, "An old man is coming up; and he is wrapped in a robe."
"And Saul knew that it was Samuel, and he bowed with his face to the ground, and did obeisance."
"Then Samuel said to Saul, "Why have you disturbed me by bringing me up?"
"Saul answered, "I am in great distress; for the Philistines are warring against me, and God has turned away from me and answers me no more, either by prophets or by dreams; therefore I have summoned you to tell me what I shall do."
"And Samuel said, "Why then do you ask me, since The Lord has turned from you and become your enemy? The Lord has done to you as he spoke by me; for The Lord has torn the kingdom out of your hand, and given it to your neighbor, David. Because you did not obey the voice of The Lord, and did not carry out his fierce wrath against Amalek, therefore The Lord has done this thing to you this day. Moreover The Lord will give Israel also with you into the hand of the Philistines; and tomorrow you and your sons shall be with me; The Lord will give the army of Israel also into the hand of the Philistines."
"Then Saul fell at once full length upon the ground, filled with fear because of the words of Samuel; and there was no strength in him, for he had eaten nothing all day and all night." (1 Samuel 28:13-20 RSV)
It's also very important to note that Saul used a witch (1 Samuel 28:7) to consult that spirit, something that God commanded never to do:
"There shall not be found among you any one who burns his son or his daughter as an offering, any one who practices divination, a soothsayer, or an augur, or a sorcerer, or a charmer, or a medium, or a wizard, or a necromancer. For whoever does these things is an abomination to The Lord; and because of these abominable practices The Lord your God is driving them out before you." (Deuteronomy 18:10-12 RSV)
Are ghosts angels then? Righteous angels did appear to humans quite often throughout Bible History, but they never did it in a "haunting" or obscure manner. They usually appeared in the form of humans, who identified themselves in a clear and dignified manner, while bringing a message or on a mission from God. There was no nonsense.
So, if "ghosts" do exist, and they're not humans (see What Happens When You Die?), or God's angels, what's left? Demons.
Demons are fallen angels who have become warped in thought and behavior. The very small number of "unexplainable" incidents (keeping in mind that most sightings are honest misperceptions, deliberate fabrications, or unhealthy delusions by the mentally ill or those impaired by alcohol or drugs) are very likely demons. And they are nothing to worry about for the converted Christian.
Fact Finder: How did the people of God cast out demons? See Casting Out Demons