I knew my childhood best friend - who moved 300-odd miles away when we were teenagers - was pregnant... before she did. I had a dream that we were walking out of the church she got married in, with her carrying a baby girl. We'd not seen each other in years, and only communicated - at that point - through FB messaging. She wasn't trying to get pregnant, she didn't know that she was pregnant. And I didn't tell her about the dream until a week later when she sent me a message saying that she'd just taken a pregnancy test and it was positive, and how delighted/excited/scared out of her mind she was.
She had a little girl (who is now 8 years old).
When they had the gender-revealing scan, my friend said that she felt very much as though she didn't need to go - because I'd said, a couple of months earlier, that if my dream was right, she'd have a girl.
That's the oddest "thing", but there are a whole boatload of others.
So do I believe in psychics? Well... I believe that it's best to keep an open mind, because we simply don't know. However, I'm descended from the 7th son of the 7th son on one side, so... who knows! 