I've thought about sharing this before, but I don't like telling people. I'm a skeptic by nature, but some things are just unexplainable.
My grandparents house is next to a cemetery. There is a bit of space between the house and the graves (large yard, ravine, and then the bandstand for Memorial Day before you get to graves). I've never been afraid of it, partially because I was taught at a young age it's just a place. When my grandparents passed, my mom and stepdad decided they wanted a simpler life and moved in. It's a few hours away from where I grew up.
I was visiting one night, but I couldn't sleep. I stayed in the basement bedroom, but there was something that was bothering me. I then noticed a light in the main room (that the bedroom connects to, the door was open). I looked, and saw a green ball. I don't know how else to describe it. It was fairly small, but moved
very fast. It was glowing, almost like a dark neon green. I would see it fly across the doorway, disappear for a few seconds, and fly back the other way. I thought I was seeing things.
Until it came into my room. I was scared, but more of a 'what in the world' than 'I'm in danger' scared. I pinched myself (enough to leave a mark for the morning) to make sure I wasn't dreaming. I even thought my eyes were playing tricks on me. I put my hand about an inch from my face, and I could still see the ball flying around the edges of my hand. It seemed like it needed me to do something. It would linger in one spot by the doorway, like it was watching me, and then zip all around the room again. I honestly don't remember if it went away or I went to sleep.
The next morning, I asked my mom if she had seen anything odd in the house. She put down what she was doing and said, 'you've felt it too?' That is VERY unlike my mom. She's seen glimpses of things, and often felt like something is watching her. She then bean dipped me, changing the subject.
Before my parents moved in officially, they rented the house for a few months to some friends who lost their home in a fire. The wife took me aside once and told me the house is haunted. She always felt like something was watching her, and didn't want to go back. This woman is like the towns first lady, and doesn't do anything that may affect her reputation.
I don't really know what the deal is, but I've never been afraid there. I do believe there is something, possibly because of the proximity to the cemetery. I moved in there for a while and never saw the ball again. My cats, however, acted very strangely there (even for them). They would chase things that weren't there, hide for no reason, and be staring for a long time at nothing. I've had these cats for 6 years, and when we moved out, the strangeness stopped. Well, some of it. They are cats.

I feel a little silly even saying this. My first apartment was in a very old building. I had an issue with the ceiling fan and closet. I hate ceiling fans. Every day, I had to turn it off because it somehow turned on. I would leave for work, make sure it was off, and come home to it working again. I told my neighbor, and he said 'oh, it's the ghost'. I rolled my eyes, and he said, 'no, just ask her to stop.' My first conclusion was that someone had a key to my apartment and was messing with me. But a few days later, I said outloud, "I really hate this fan. It always blows my hair into my face, and I can't sleep. Could you please leave it off, at least at night?" It never came on again.
Then the closet door started opening. This isn't just a regular door. The knob is a deadbolt, you really have to turn it to get it to open (the fuse box/hot water heater were in there). The door would be open every night when I got home. This time, I said, "I know you're here. Thank you for the fan. Could you please leave the closet door closed? I don't like having guests over and having them see everything. I know you're here, you don't have to keep reminding me." It stopped. So did the strange things.