First of all, I'm not a 'spiritual' person, I don't believe in much of anything that science can't measure and to some degree explain. I'm not religious, superstitious or even really 'interested' in what's called the paranormal. I'm intrigued by anything I can't explain to some degree, but it's an objective, scientific sort of interest.
When I bought the house I live in I spent a few nights sleeping on a mattress and just working all day getting the place ready. It was easier for me to spend the night than go back home and return the next day. As you can imagine I was tired at the end of each day, wanting nothing more than to crash out and wake up refreshed to get back to work. One of the items apart from tools and stuff I had in the new house was a battery powered radio which I still have. It's a very cheap simple type, water resistant, intended for bathrooms. The on/off is a pot with a switch on it. The click is very firm, and the pot is quite stiff to move. The first or second night I was about to fall asleep and the motion detector for the lights in the hall flipped on. As it was simply a cheap PIR type, I figured it was either temperature displacement setting it off or just a little ripple in the supply. It happened a couple of times before I had enough and killed the power to it. Note, I'm used to this stuff from having dogs that will wander around at any time of day or night. As I was completely alone, I found it uncanny but probably just a malfunction or trigger happy detector circuit. Then, after laying down I muttered something like "well, whoever else is here - I'm in charge now, ya better start paying rent". After a couple of minutes, the radio turned on. This got me startled as I knew that I firmly clicked it off, plus even if it slipped over the 'notch' of the switch, the volume would still be at minimum - not a level I could hear a floor away. So I got up, found the radio still hanging on the wall - but on. I turned it off making triple sure it was properly switched. After laying down again, it happened again. At this point, I had no plausible explanation anymore - I'd checked it myself moments ago. I went to the radio, turned it off and loudly stated something like "OK, if there's someone here we're going to have to co-exist and work this out - cause this place is mine now...?". Nothing, no response. The radio remained silent, it's never done it since. I did however dismantle it just to check if there was SOME way it could have simply 'sprung' into action. Nope. I've heard some footsteps in the house since, but when you have pets walking about that's pretty inconclusive. No other weirdness whatsoever.
I've had a couple of other weird experiences, but nothing really tangible like this one. To this day I have no idea how that happened.