The biggest coincidence that's ever happened to me was about 8 years ago when a friend of a friend visited Manhattan from England and my friend put us in touch. Her name was Michelle. We went out for dinner a couple of times and then she went off and did her own thing for a couple of days. At some point I was walking a dog on the Upper East Side when an old lady stopped me to pet the dog. We got to talking, and she asked me where my accent was from. When I told her Newcastle, she said "oh, I was talking to a young girl in Central Park earlier and she said she was from Newcastle. Lovely girl. Name of Michelle." I asked the women her name, and she said it was Betty. So later I called Michelle and said "Have you been talking to Betty in the park?" Really freaked her out. In a city of 9 million people, this old lady stops to talk to a random girl in the park, and then that same day, all the way across town, she stops to talk to a random guy and it turns out it's a friend of the girl. I really should have put my lottery numbers on that week.
Another weird thing happened to me a couple of weeks ago, albeit sadly. 20 years ago I worked with this really nice guy for a year or so and we'd have some great conversations on the job. He stood out in the place because everyone else seemed to be a lowlife or ex-con of some kind. Anyway when I left that job I never saw him again. 20 years later he pops into my mind, don't know why. So I figured that maybe I'd look him up on Facebook and get in touch. Trouble is, it's such a generic name that it's like looking for a needle in a haystack. I'm scrolling through hundreds of results, ignoring the ones which don't have a proper profile photo because I don't have time to click through to them all. But then a profile appears with a photo that's just a hand with a wristband on it. I don't know what made me click through to it, but looking through the person's photos I could see it was him. Success! He looks older obviously, and has gained weight, but it was definitely him. So I'm about to send him a "remember me!" message, and noticed all of these "RIP Malcolm" posts on his wall. He'd died the previous day! Couldn't believe it.