I've been to several psychic nights, and occasionally I have been approached. I know that the majority are cold reading me, but I am not going to these nights to try and 'prove' anything - I just find them quite entertaining.
One experience however did stand out, and has made me wonder whether there are people out there with some unexplained gift.
I saw someone in a private home, he was a friend of a friend of a friend and he rarely did readings and took no money. He asked to hold a watch or ring of mine.
Just for some context; I have moved around the world with the forces my whole life and at the time I was new to the area - nobody knew me or my family history. I have a very (very) british name, but my mum is foreign, I have a 'forces' accent.
He told me that my grandfather had come through to him, specifically my mum's dad. He told me his (very foreign, very unusual) name. He told me my mum's (very foreign, very unusual) name. He told me that he used to walk with my mum on his shoulders through an apple orchard when she was little. He said that he'd been a terrible father, but that when he died he wanted to make it up to his daughter and so looked out for her and her kids. He told me what my mother had put on his coffin. He said that my dad was having an EA and gave the name of the woman. He looked at me and said, 'you're wondering how I can understand him seeing as I don't speak X, and he never spoke English' and then said that he couldn't explain it, just that language is not the same in the spirit world.
This whole time he was twirling my ring in his hands, and I hadn't said a thing.
If this guy was cold reading me, he was spectacularly good. This was in the infancy of the internet and as I said I was not local to the area. My maternal grandfather died when she was still a very young girl, but I'd heard stories about him. When I asked my mum about all the details of this reading, she went deathly white and he had been right about it all. She confronted my dad about the EA too, and he admitted it. They worked it through and to this day, my mum says that 'her dad' saved her marriage.
This is the only experience I've found difficult to explain - the rest are fairly easy to debunk.
After I lost my dad there were a few readings where the medium spoke about him - I don't know if they were genuine or not, but it did give some comfort. As far as I am concerned, as long as they are not exploitative or harmful and it gives people comfort, then I am good with it.