To believe in an objective difference between right and wrong (God and not God) implies the existence of immortal souls, spirits that exist non-physically, and continue existing even after the mortal physical body dies (naturally becomes unable to continue living in the physical sense). So, in this sense, ghosts do exist. We are, in fact, part-ghost right now, in the way that “ghost” means a non-physical spirit.
But, as humans, it is often tempting to “humanize” our understanding of the nature of immortal souls so that they are understood to exist as humanly as we do now, just without physical bodies, as if they’d float around the physical world and communicate with and/or frighten us physically living people.
This makes no sense. Think about the nature of truth; when something is true, its truth exists outside or beyond the physical constructs of space and time. Its existence is not dependent on a specific location or time the way that physical phenomena is. So it is with the difference between right and wrong, and so it is with God, and so it is with our immortal souls. When our souls separate from our physical bodies, they also separate from the physical constructs of space and time. We can understand this to be true even while it is currently impossible to understand what that sort of existence is like. But it does allow us to understand how the common notion of “ghosts as spirits wandering around the physical world” is at best a silly notion of spiritual ignorance, at worst a temptation away from God (truth).
So a lot of “ghostly phenomenon” does not pass the true-faith-in-God test. Ghost Hunters and such shows may be entertaining, but to truly believe them is to reject the true nature of God, whether it be for the corrupted desire for unnatural powers (that is, the desire to communicate with the dead; not because it can be done but is just dangerous (it can’t be done, but we can easily spiritually deceive ourselves into believing it can, like a spiritual placebo effect, through which we can credit perfectly natural mental abilities (such as talking to oneself) to ghostly activity), but because the desire for that sort of experience is not in union with a desire for God (love and truth)), or simply out of a spiritual misunderstanding of the nature of God and immortal souls (as opposed to the incomplete understanding of the nature of God we all naturally experience as part of our temporary physical existence).
That said, we know that God can interact with us in our physical existence through our non-physical spirits; otherwise we would be incapable of understanding that there exists an objective difference between right and wrong, and would be incapable of believing in Him. (I am considering our “sense” of God as a form of “interaction” — I do not mean to imply that God often physically moves things around in front of us to prove His existence to us — He obviously doesn’t — I do not think He would desire for our faith in Him to be based on tricks of changing the laws of physics, which would probably do more harm to us than good.) God must also, then, be capable of allowing, in proper conditions, the spirits of the physically departed to spiritually appear to or communicate with physically living beings for the sake of the spirit of the physically living (not for a ghost’s “unfinished business”). It is also important to note that, when this happens, it happens through and with God; it is not some departed spirit acting of its own volition, and it is never done in response to a living being requesting or desiring such contact, which, as I stated before, is a spiritually disordered request.