Ghosts: Yes. While I haven't seen one myself, I've known several people who have, and most of them I trust (including my mother).
And while it wasn't quite a ghost, I did experience something of a crisis apparition* of my late great uncle. At the exact moment he died, I and my parents (and my dog) heard a very strange noise coming from the middle of the room. Sort of a thud or a bang, like something had fallen on the roof. Except it didn't come from a roof, it came from about 2 feet below it.
At the time the sound happened it was just a bit eerie. But when my father (who would be my great uncles closest relative) got the phone call that my great uncle had passed away, and the time of death, it was just plain creepy.
ESP: Depends on which sort
Demonic possession: No. Maybe possession by something, but not demons, since iI don't believe in them
mind over matter: That's kind of vague. If you mean something like telekinesis, no.
* A crisis apparition is when someone sees the ghost of someone they know right around the time they die