The single weirdest one for me was when I was in the Army. It was in the early '90's; and we were in Wainwright Alberta; spending the weekend in barracks; the last weekend with a roof before five months in the field.
I was on my bunk, reading a Dale Brown (I think) thriller, while a friend had Pink Floyd playing on his little radio.
In the book; one of the characters was lamenting the death of his wife; and it went like this: "'Vera!' he thought mournfully, 'Vera, what have I done?'"
At the exact moment I read the words 'Vera, Vera'; on the radio Roger Waters wailed, "Vera! Vera! What has become of you?"
I had to sit up and go 'Whoa!!!'

Another weird one: I was giving a self-defence seminar in Virginia; having been called down by a local aikido dojo. There was one young lady there who was pretty inept - not having done anything like this before - but eager. After the seminar we were chatting a bit; and I dropped for the first time that I live in Kitchener. Her jaw dropped, she told me she thought I was from Toronto; an hour away. "Nope, Kitchener," I said. "Why?"
"I come from Kitchener too! I'm just down visiting friends for the summer!" Her friends had dragged her out to my seminar for kicks.
And if THAT'S not weird enough for ya; it turns out she works in the same building I hold my defence classes in. (She's now a student. )

Yet another weird one: A new pressman started at the printing company I worked at a few years ago. He was being trained for that machine by a senior pressman. I was on the deck when they were talking; and the senior guy started complaining - as blue-collar schmucks will - about how his Ex was a b**** who nailed him with heavy alimony. The new pressman agrees, saying his ex did the same thing. After a minute; it comes out: Everyone say it with me now.... same woman. Weird, eh?