I don't believe in ghosts but, like NoMercy, I've experienced something that was at least 'odd' if not 'unnatural'.
My mother was ill for many months before she died of cancer. Although I visited her in hospital as often as I could, it was inevitable that I wouldn't be around when she actually passed away.
One evening I received a phone call from an ex-pupil of mine, who had later become quite a close friend, but whom I'd not heard from for many months. She said that she was wondering how I was coping with the knowledge that my mother was close to death, and she just wanted to let me know that I'd always got someone to talk to if I needed it. She said that she wasn't really certain why she'd called but she just felt she ought to.
Later that evening, my father phoned to say that my mother had passed away. When I asked him about the time, I realised that my friend had felt the urge to phone me at exactly the same moment that my mother passed away.