"Ghosts" and associated phenomenons definitely exists.
I used to work either alone or in a pair, late evenings and nights, in a haunted (widely and generally recognized as such) building, for years. There's absolutely no doubt in my mind. There were so many things going on that it became routine. One would hear the sounds of doors open and close, footsteps... I would often see - in the corner of my eye - or sense/hear someone coming up behind me or from the side. Then I would turn around, expecting to see whoever had come back and sneaked into the house, and there would be no one there. Sometimes I would be busy and ignore it, and get a really solid sense of someone standing behind my shoulder, observing what I was doing. I would even see reflections of it in glossy surfaces in my field of view. But when I would turn around, there would be no one there.
Edit: There's one thing I want to be very clear about. This was not just "me"! Everybody who worked night or late there, had similar experiences. When I was new, and once had to work overtime, my immediate boss looked at me and laughed lightly and said: "Look, there's a thing you should know. This place is haunted." Then he laughed lightly again, but added: "I'm serious."
Years later, I decided to approach a new employee who were also - then - working nights: "Umm, ...have you ever, ...like, experienced anything funny, like ghosts, like?" He stared at me and burst out: "- Are you kiddin me! This place is like Poltergeist!".
So no, it wasn't just me. I'm not nuts.
So I don't doubt the phenomenon, since I've personally experienced it so extensively. Where it then goes wrong, is that I really don't see any reasons for jumping to the conclusion that it's the spirits of dead people. And then build an entire card house of increasingly detailed superstitious beliefs, based just on that.
Just because you believe in A, or A is a fact, doesn't mean that an entire train of utterly unsupported and dissociated B to Z also need to be accepted. People fall into that trap all too often.
"Do you believe in God?", "Okay, then you need to hear what this holy man has to say, and then come along and help killing God's enemies".
"Look at that, it doesn't look like an aeroplane does it?", "Okay, then it must be an alien space ship full of green or gray men on a mission to anal probe someone."