I'm not familiar enough with the term "paranormal," learning it only from book and TV titles. I do, however, believe in the Supernatural. I believe in God, how can I not believe in the supernatural? I also believe the majority of the reports of supernatural, etc., in the Western world, at least, is false. Our post-Enlightenment world is so focused on hard scientific proof, that it is generally much easier for the Devil to do his job without dragging in fantastic supernatural performances.
That said, witchcraft, Ouija boards, and other thrill seeking encounters with the supernatural are only ever a dangerous invitation to the demons out there. We are strictly commanded not to meddle with magic of any form, for very good reason. Do not ever give demonic powers any opening.
But we as Christians are also given power over the demons, in the name of our Savior Jesus Christ. I've known of pastors who have exorcised demons. I have friends who have been harassed by demons, though not possessed. There is no power we have greater than to call on the name of Jesus Christ.
As for the divine supernatural, I believe that too, happens. I know a person who has, once, heard a literal voice from God telling him what to do. One of my friends also has a relative who dreams of events he could have had no way of knowing - for example, he might tell his cousin the next day something along the lines of, "I dreamed of you last night, how you got drunk at this friends house and spent the night with your boyfriend and this is what happened." He keeps the actions of his loved ones in check by always knowing. I'm sooo thankful I do not have a prophetic gift like this.
I've also once sat through an entire service debating a question with myself (and hearing little of the sermon). In his concluding prayer, the pastor addressed the very topic directly, saying, "I'm not sure why, but I feel the Spirit laying this on me, and I will say it." The words were clearly meant for me, though the pastor did not know it, could not have known it. I also know that it could not have been meant for any of the other 8 people at that itsy-bitsy church. Thank you, God.
I have heard too many instances from people I know and trust to doubt the existence of the supernatural, even though I am naturally inclined to doubt.