Maybe not paranormal, but I've never figured out an explanation.
One time in grade school, I was playing chess against another kid. Yes, I was a nerd; you knew that. This was during "free time" (like recess, but indoors and only 20 minutes), so other kids are doing things, and some are gathered around watching us. As I was considering my next move, someone behind me starts talking, telling me what to do, which is annoying so I turn around to tell him to shut up... and there's no one behind me. No one anywhere near me, and actually there's a wall behind me so it's not like someone could've been playing tricks on me. But I heard his voice very clearly, just behind me.
My favorite WTF story was told to me by my best friend John. If there's anyone who is honest to a fault, it's John, so I believe this story 100%.
This is also from back when we were in school. After school, he was tired, so he went to his room and took a nap. Dreamed that he was walking home from somewhere, and noticed that there was this car following him, slowly. He started walking a little faster; the car sped up, keeping just behind him. Now almost to his house, his decided to run for it. Just as he gets to the front door, he hears gunshots, and (in the dream) feels two bullets hit him in the back. He falls and...
The phone rings, waking him up. It's his sister, who's a lot older and had moved to California. With not much money, she lives in a kind of crappy part of town. She asks if Mom or Dad are home, but they're both at work. Of course, yeah. But she's kinda freaked out and needs to talk to someone. She was on her way home from work just now, and someone was following her, so she ran to a neighbor's house, and just as she got in and closed the door, they shot at her. Two shots.