Ok, here are mine:
In disney world, we ran into my little brother's first grade teacher in a switch-back in line for Thunder Mountain Railroad.
My boyfriend took a climbing course a few years ago in Asheville. We've since run into his guide at the REI in Asheville (not too shocking), on a random ice climb in a remote climbing area of New Hampshire two years ago, and then again in New Hampshire this year on the beer isle of an off-the-beaten-path grocery store.
Ran into... can't remember his poster name, but R.D. (initials... 'the boards' funded his trip back to the Orange Bowl) on the steps of the British Museum while studying abroad.
While studying abroad, I made friends with a couple guys from another school who were also studying abroad in Salamanca. They were going on their two week fall break, just traveling around on eurorail passes. Didn't have a real plan when they set out, just figured I'd see them when they got back. During that time, I went to Interlaken, Switzerland. While walking back to my hostel the second night in town, I was taking a shortcut through a neighborhood back road and I saw the silhouette of two people approaching. I was going to put my head down and just keep trucking (I was walking alone), until I hear my name. It was those guys from Salamanca... so random.
I went to Rome by myself, and while touring around had a decent conversation with an older couple in St. Peter's. We spoke for a while, then parted ways. Later on that evening, I was across town and wanted to get to the spanish steps to walk around and get some dinner. I made a last-second decision to take the metro, and just barely squeezed onto a very crowded car before the doors closed. I found myself pressed up against the gentleman and his wife again. Couldn't believe it. They invited me to eat with them and I declined... to this day I still wish I'd eaten with them.
(last one) At Wake, I was filtering into Benson for some presentation and I hear my name. Looked up and see a girl who I'd been decent friends with in elementary school/middle school before her family moved to Georgia. Overall I guess it's not that random that she ended up at Wake, but I definitely didn't expect to see her.