The experiences that come to mind all involve some form of telepathy. I'll try to briefly describe the most interesting ones (both are about death, in case anyone doesn't want to read about that.).
One was a dream I had where my father and his father (both of whom I was and am estranged from, but once had a bond with) appeared in my garden. They implied that my grandmother was dying, and that she was "waiting for me". I knew she'd loved me a lot so this wasn't too surprising a thing for them to say at the time, our estrangement was against both of our wills I think, but the symbol they used to communicate that she was dying wasn't understood by me to be that at the time (when my grandfather said she's waiting for you, he procured a tiny doll and pulled it's head off). So since I didn't make the connection, I didn't try to visit them. It had been over a decade since I'd even talked to them and I may as well have still been a kid at the time. I was waiting for them, too.
I later found out that she had been dying at the time of the dream, from cancer. She died not long after. I had no way of knowing this until after the fact, as I'd had no connections on that side of my family for years.
The other one happened when I was awake reading a book, a close friend of mine committed suicide in his home and at the time that he did it I felt something extremely bizarre that I've never felt before or since. It was what I can only describe as a kind of cerebral jolt. As if my mind, and only my mind, had been yanked to the side. I was sitting perfectly still but my vision jolted with it, a little bit similar to how a TV or monitor's display might jolt in a certain direction when the power cable isn't properly connected. It was also accompanied by a very subtle, almost imperceptible crackle in my head. Vaguely electrical. This all happened in an instant. Easily less than half a second. I didnt feel any different afterward, nor did I have a bad feeling, I was just sitting there perplexed and astounded. I found out the next day that he had died at that time.
I do have something of an explanation for these experiences which I believe, a hypothesis really: that what we call bonds are far more real and literal than we think. That they are what allow these synchronous experiences and telepathic transfer of information between people. I think that's what allows things like telephone telepathy too - when you spontaneously think of someone you know and then half a beat later your phone is ringing and it's them. That's an experience lots of people have apparently. I think what happened with my friend might have been a severance of our bond, because he died. Or a very radical transformation of it into something that might not look much like a bond anymore, if we could see it.