I have two strange/creepy unexplained events that stick in my head.
The first happened when I was teenager, my DF ran his business from our family home and we had a phone/fax machine in the living room. Whenever we picked up the phone we could always hear a radio station playing very distantly on the other end. I'll never forget the time I picked up the phone to ring a friend and could hear Penny Lane playing!
The other is slightly more sinister. My DM and I were at home alone one evening, it was summer and still warm and I had the bedroom window open. I can remember hearing a loud crash in the garden, thought maybe the cat had knocked something over and thought little of it. Then my mum suddenly popped her head around the door told me that she was going to bed and that she'd "locked all of the doors". Thought it was an odd thing to say, but thought little of it. That night I was kept awake by the next door neighbours security light going on and off, and when I got up the next morning my DM pointed out that the garden ornaments and solar lights from next to the fence had been smashed.
That's when she told me that she to and heard the crashing sound the night before, and got up to investigate and when she looked through the kitchen window she was convinced she could see a person peering through the window, as as if they were standing next to it with their back against the wall and peeing in from the side, but wasn't sure if she was seeing things or not! She was scared enough to lock all of the doors, but not to ring he police it seems! Still freaks me out now! I'm sure someone was in our garden for whatever reason!