We moved into our first house when my daughter was 18 months old -- a 75 year old fixer-upper. Shortly after we moved in, strange things began to happen. The usual stuff like doors opening & closing by themselves, lights turning on or off, footsteps,etc. Although we knew there was something odd, our two cats and dog never seemed disturbed by it, so we didn't worry too much. A couple of incidents, though, shook us up more than others.
One afternoon while my daughter was napping, my husband sat down to watch some TV in the living room. The ceiling fan then turned on and off by itself. He just heard the whirring sound and as he looked up to see it spinning, a large picture behind the sofa fell off the wall, slid down, hit the back of the couch before it keeled over and whacked him on the back of the head, producing a nice goose egg.
The scariest incident -- my daughter woke screaming one night just before she was two years old. When I went in to see her she climbed me like a monkey would climb a banana tree, all the while talking in a strange gibberish (she spoke very well for a toddler). Her arms and legs clung to me so tightly I thought she'd leave marks. Every time I'd try to put her down she'd become frantic, chattering all the time in this gibberish. We brought her into bed with us where she sat straight up, all the while still talking gibberish, and whenever we tried to turn out the light she'd screech. (By this time I was starting to get a little freaked out and was waiting for her head to start spinning and spewing pea soup.) Suddenly, she became lucid and simply said "Mary ... Mary is dead" and then continued talking gibberish. My husband asked if I heard what she said and I told him I'm sure we must have heard wrong, but we both heard the same thing. At this point, I didn't want her even in the same bed as me!
Eventually he calmed her down and she went back to sleep. The next morning I asked her who Mary was and she looked at me like she had no idea and said "I don't know, but Mary Poppins is on TV." She had no recollection.
She would also spike these high fevers for no apparent reason (like kids do). However she'd see and talk to people that weren't there. She'd look right through me and say "Mommy, who's that man over there", and I would just freeze.
The last thing to ever happen (at least that I'm aware of -- I asked my husband NOT to tell me if there are any new experiences) was one night just after we went to bed. Our dog slept in the kitchen -- we'd close the door to the basement and block the doors to the hall and to the dining room to keep him in. As we lay in bed, we heard the distinctive creak of the basement door. My husband went downstairs to the kitchen where the dog was peacefully laying on the mat undisturbed. He asked if I had gone down to the basement before coming to bed because he had shut off the light and closed the door, and now they were on and open. I said I hadn't. As we discussed it, we heard the basement door again. He went down to see the door open again and the basement light back on (and the dog still resting peacefully). He came racing back upstairs, his heart beating a mile a minute and said "There's someone in the house!" He went down again carrying a stone statue as he checked every corner, every closet -- and of course no one was there.
We've been there almost 8 years and its been 6 years since that last incident. I'm not sure what to make of it, but I'm sure if there was anything to fear, we would know it by now, or the animals would react.
We did ask our neighbour about the house's history. She moved in next door as a bride more than 50 years ago, and she's seen many families live in our tiny house. She did indicate that one lady did pass away from illness/old age many years ago, but in those days they always called each other Mr. & Mrs., so she never knew the lady's first name. I'm not sure I want to know either.