Hmmm, let's see
Riding a cable car, and seeing one on the opposite side passing us...and the school caretaker waving madly at us. (But schools have many members of staff, most people have some association with a school...bumping into somebody vaguely associated with school must happen to a fair few people out of all the millions of us...)
On holiday in Europe when I was a teenager, and we bumped into another lad from my maths class. Only 4 of us in that particular class...(Still the same comment as above, but a better one...)
Popping into work, late one night, to check up on something, looking round for the staff, decide to try the treatment room "Oh, good, we were about to call you" about a patient who had only just arrived. Actually, done that quite a few times...but then, people don't remember the times you turn up and they weren't about to call you...something about selection bias on memory?
How about...when I was really young.....my brother asked my mother "What would we do if nocool died?" Okay, obviously I didn't. But I was in resus a couple of hours later....or does that belong in a spooky thread?!