Do they exist? To many it seems that they do, however when one is possessed by a demon, it usually isn't contagious, meaning that if one person is exercised of their demon, then they do not go on to prey on another person.
Based on reports, people say they usually end up coming into contact with demons usually after performing some type of hypnosis, usually of one's self. Ouija Boards are an example of this. And so it seems based on that, that demons have a high possibility of being 100% from the mind. Perhaps we all have this 'demon' and it is a part of our subconcious that we let loose when in deep hypnosis. Perhaps what we ourselves think will kill it, actual does kill it. For example, if I were Catholic, I'd typically think that a priest would rid me of my demons. Usually this is how it is ridden. You'll never see a Buddhist exercise a Mormon, nor a Muslim exercise a Hindu.
This all raises the question: Are demons just our minds acting in insanity?