I was staying in Paris many years ago, and we popped out for a kebab. Got chatting, as you do when on hols, and it turns out the blokes running that kebab shop were cousins on the local kebab shop back where we lived.
A mate of mine bumped into the secretary where he worked, in Cairo bus station. Thing is, he weren't even sposed to be in Cairo, but had been transported there from Israel, after the kibbitz he was staying on came under attack from Hezbollah or someone.
As for sharing birthdays; I was born on the 29th February, and have only met about half a dozen people in my life, born on the 29th. None on the same day as me.
I'm also left-handed, which makes me even rarer. If I ever met a left-handed person who shared my exact birthday, I'd be propply freaked out.