This isn't actually a ghost story, but it's still pretty weird. The date in question occurred (obviously) before my time, probably around 1974.

My parents were out on a date and started talking about strange things that had happened to them. My father told my mother about a hike he had been on while backpacking in Nepal. He stopped for a rest and immediately became aware of a "force" in front of, and a little above, him. He wasn't sure how to describe it--he couldn't see anything and he couldn't actually touch it, but he knew that there was something there. He said he got the impression of a big ball of energy. My mother told about the death of her mother, which happened when Mom was 22 (in 1970). She said she had sensed Grandma's spirit leave her body, and felt the body "settle". As each talked more about their experiences, they came to the realization that they had happened at just about the same time (meaning that Dad felt the "force" at the same time Grandma's spirit left her body). My parents had not yet met each other at the time these things occurred.