I grew up in a house that had a lot of paranormal stuff going on, so I'm used to it. I know it sounds strange, but I feel that I'm sensitive to this kind of thing, so my family and I have seen/heard lots of stuff over the years, both in my old house and out in other places.
The house I grew up in was built in 1964, but before that it was on farm land that had a hug fire devastate the land. Before the farm was here, it was part of a Revolutionary War-era fort, so people have been pounding around on the property for centuries. Also, by coincidence, it's situated next to a graveyard. We've had guests tell us they have seen people walk up the stairs and through walls! We had a few really strange instances here over the years. One involved us asking whatever's here to turn on lights and it would on command. We would ask it questions, and it would turn the lamp on or off. Another thing that happens is that family members will hear each other calling them by name, but the family member calling them will either be out or in some cases right next to them! One time, my dad and I heard my mother calling us from upstairs, and she heard me calling her from upstairs. We were all in the basement family room standing talking around our bar, right in front of each other!!!
Outside of my house, one the strangest things that I've witnessed happened in Hull, MA while going to visit my grandmother one winter night. Hull is a town located on a peninsula, and is hopping in the summer and very dead in the winter. My uncle lives right on the ocean there in a huge beautiful old stucco 3-story house that has had some interesting owners, including turn of the century entrepreneurs as well as people that later ran a boarding house out of it. My grandmother lived with him there, and at the time, my cousins were away at college and my uncle was away in Italy visiting friends, so my sister and I were heading over there to bring dinner to my grandmother one night and spend some time with her. We turned down their street, and my sister and I see this woman in a white flowing summer dress and giant white hat, like something you would see on a rich woman in a movie based around the turn of the century. As we got closer to her, she started to sprint. My sister and I then see her take a turn into my uncle's driveway and into the back yard, so we floor it, pull in, and get out to look for this woman. The back yard that she ran into was fenced in and there was fresh snow on the ground. There were NO footsteps in the snow and no evidence of the woman being there at all!!! Years later, we were there at a summer BBQ, and we were talking with our now-adult cousins and many of their friends. We got on the subject of ghost stories. You wouldn't believe how many of them saw that same "lady in white" wandering around the property over the years.
I have many more of these stories, but I'll quit while I'm ahead here....