Happened to me once. I was making Xeroxes in a copy shop (!) and the machine was right inside of a big window.
Glancing out, I noticed a ginger-haired woman at a bus stop across the street, who could have been my twin. Thought I was imagining it.
The shop manager, who knew me as a regular customer, came over to see what I was gawking at. He agreed, she was my twin.
She was even wearing the same style sunglasses and trenchcoat that I usually wore, although I was dressed differently that day.
It was a twilight-zone moment.
My wife bumped into mine one late night.
I received a frantic phone call, five minutes later, as she had kissed me goodnight, while I was on the PC, just before laying down to bed, when she later realized I was some 70 miles away.