Stuff like this has actually happened three times in my life. Here's the most unusual one:
Took a vacation from work to plant a lawn at my newly constructed house in a city I had recently moved to. Went to a nearby gravel/dirt yard to order delivery of topsoil. Guy came out and took my order. Filled out the form, asked for my name. It's an unusual name, and I started to spell it for him. He said, "I know how to spell it." He put the clipboard down and said, "Just a minute." He walked back into the office and came out with his business card and handed it to me. We had the same (unusual) last name and his first name was very familiar to me because all my life people I had just met back in my hometown (big city) would ask me, "Oh, are you so-and-so's brother?"
Over a 25-year span, I had been asked that question dozens of times. People said, "You look just like him." I tried to look him up but he had moved away. After that, whenever people asked if we were related, I'd ask them if they knew where he went, but no one did.
So here we were in this small town several hours from where we grew up, and he's telling me, "I used to get your mail." We did look a lot alike. We made arrangements to grab lunch together. He brought a family-tree book with him and we looked up all our old relatives. Turns out we're distant (very distant) cousins.
Wish this had a happy ending. As you probably guessed from the geneology reference, he's a Mormon. I was a slave to dubdom, so of course we couldn't hang out together. Years have passed and we've lost touch.