I'm actually going to be travelling on Monday, so I thought I'd post something now. Shakespeare's birthday is widely considered to be April 23, which happens to coincide with the day that he died(*). The only similar occurence of which I'm familiar is the famous Mark Twain / Halley's Comet connection, where he "came in and went out with it", in Twain's own words. It wasn't the same day, though. But still a neat bit of trivia. While I'm on Twain I might as well link to Is Shakespeare Dead? by Mr. Twain himself.
Anyway, back to the Bard. I wish I lived someplace where they celebrate his birthday with parades!
(*) Records indicate his baptism as April 26, and at the time Christenings were done 3 days after the birth. So April 23 is a convenient guess, like much of his biography.