The question isn't do you believe Ghosts exist...but If you do Believe in Ghosts, what do you believe they are...because there are many theories in that regards...and many believe it is religious based.
As a Christian I can tell you some of the theories that many Christians believe.
A)Ghosts are the souls of the dead waiting for Christ's second coming so they can go to heaven or hell which ever they are called. Many Christians believe that when the trumpet sounds the Dead will be raptured first like scripture says and until that time their soul's or spirits can wonder the Earth. Although, many also believe that our soul's immediately go up to heaven so Spirits must be human's that aren't Christian or something else.
B)Others believe that Ghosts are demons or fallen Angels, (they are not necessarily the same thing) and that these Demons will do anything to keep the truth about Christ from people of Earth. In this they form themselves in the image of Ghosts and Spirits, or even Aliens to trick people into believing that Christianity must not be real because Ghosts and such exist. I personally, believe this is possibly true with Aliens but very narrow minded in Ghosts.
I believe in option A. The Bible even has a story of a King going to a witch doctor to call up a deceased prophet of God, whom was shocked that the King would go to such obviously immoral means to get advice from the prophet.
This to me speaks that the spirit world is alive and can be manipulated by the physical world and vice versa. We do not know where our spirit goes when we die, but if a soul or spirit exists, I believe it must follow the rules of matter and yes science which states matter can neither be created nor destroyed...once a Soul or Spirit has been breathed life, I do not believe it dies, and therefore when the physical body is gone, that soul may find itself acting as what we would call a ghost.