We have a limited understanding of things going on in reality; we also only interact with a very small number of dimensions (scientific proofs demonstrate the existence of at least several times the ones we see -- more in the 20's at least -- with the possibility there are in fact an infinite number). Each dimension sees things happening incompletely and imperfectly. Imagine removing our understanding of time, in the middle of a ball game. In a stopped image, we would see a ball hovering midair, and would be forced to conclude that gravity does not apply to small, white balls. Personally, I think we have the same view of the universe: things happen we cannot understand or explain -- and there are a great many things going on that we can't explain at all -- because we have imperfect information. My father in law firmly believes that humans span all these other dimensions, and our actions here -- and existence, or end thereof -- are only a small part of that which is Us. I find comfort there, and afterlife aside I have to admit that current science does solidly confirm we're interacting with reality in ways we have no idea about. So there is room for clairvoyance, telekinesis, and apparitions in all our mathematical models.

Personally yes, I have had at least one real experience: we're quite sure that my father in law's house is "haunted." On several occasions, various people have heard a woman open the door and enter, and call out a greeting "I'm hoooome!" I didn't believe it personally, despite several people hearing it on several occasions, one without knowing the story at all, until I heard it myself. Sitting on the back porch talking to the family, I heard the greeting very clearly -- enough to say, "I think that's Jenny" and go greet my sister in law, who I thought it was. On all these occasions -- including my own -- the dogs were the first ones to react, jumping up and racing straight to the front door barking greetings. So there's definitely SOMETHING going on, although random hello's don't seem terribly ominous.