I've only had one experience thus far that I would judge as being far enough out of the ordinary to potentially label as supernatural. It's not nearly as elaborate or fantastical as many of the stories I have read on this site, but it is as honest of a recalling as I can give.
When I was younger it was not uncommon for my sister and me to spend a week out of our summer at our aunt's house. At the time of this particular visit, my aunt was living in Alabama with her husband and three children. I'm not exactly sure exactly how old I was at this time as summer visits to my aunt's house were semi-regular occurrences; however, I do know that my sister and I were old enough to watch our three much younger cousins, two of which are on the autistic spectrum, alone. My best guess would be that I was around 14 to 16.
Although my aunt no longer lives in the house, and hasn't for many years, I can still recall the layout of the house clearly. Nearly all of the house was on the ground level with the exception of a single upstairs room with an attached bathroom. The staircase to get to the room wrapped around the room so that there was a small landing from the door of the room overlooking the living room below (it wouldn't have looked too unlike a flipped upside down capital L). You could see the door of the room clearly from the living room and vice versa. Additionally, as my cousins were very young at the time, at the bottom of the stairs there was a baby gate.
The upstairs room was largely unfurnished (I can't remember why, but I think it was because my aunt's family hadn't been living there long). Nevertheless, my aunt had set up an air mattress for my sister and me in the room because she thought it would be nice if we had our own private bathroom.
On one of the nights of our stay, I decided to turn in early. The room had a window with no curtains and it was still light enough outside that the entirety of the room could easily be viewed. I was lying on the air mattress turned towards the closed door to the room waiting for my sister to come up to bed. I remember distinctly thinking to myself that door handle was going to turn.
Despite thinking so, I was actually very alarmed as I watched the circular doorknob slowly start to twist. Before I could even stop to ask myself if this had just been a figment of my imagination, the door handle started rapidly twisting back and forth as if someone was frantically trying to open a locked door.
Figuring my sister was playing a prank on me, I wasted no time in getting up and opening the door. No one was on the landing. Below in the living room, I could see my sister chatting with my aunt. I quickly turned, headed down the stairs, over the baby gate, past the sleeping children's room, and into the living room to join them.
When I questioned my aunt and sister, they confirmed that no one had gone upstairs. Even if my sister might be willing to lie to me, my aunt would not. She said my sister had been with her the whole time and I believe her. It is highly unlikely, though maybe not impossible, that I wouldn't have seen someone on the steps in the time it took me to get to the stairs especially because of the baby gate at the bottom. My aunt suggested the air conditioner had moved the doorknob when I told them, and I dropped the issue as not to upset anyone. I have serious doubts that even a direct gust of air hitting a doorknob directly could cause the type of intense movement I witnessed.
The only possible solution I could come up with (I've thought about it quite a bit) for the handle's aggressive movement was that possibly that the family's cat was trying to get into the room. I have my doubts about this as well. For one thing, during my rush to get downstairs I never once saw the cat which would've had to jump the baby gate at the bottom, but cats are fast so I won't rule it out. I'd be surprised if an animal that determined to break into a room ran away when granted access. Even if my opening the door had caught it off guard, I should've seen it run away. Another issue I see is that the door swung inward into the room. To twist the door handle to that extent, the cat would have had to have been resting its weight on the door and the door would've likely given way and opened. I was never given any indication that my aunt's cat could open doors or had a habit of doing so, but I've owned a cat before that knew how to do this so it wouldn't be out of the question.
I don't really know if this experience even counts as supernatural, but it was certainly strange at the time. Oddly enough, I never felt afraid during the whole event or even afterward when I returned to the room and I'm far from immune to getting scared. The only thing I'm sure of is that I didn't imagine the handle turning, but what turned it I can't say.