According to parish records, William Shakespeare died on April 23, 1616 (he was buried on April 25th).
Traditionally, people say he was born on April 23, 1564. Actually, since his family and community didn't realize he was going to be THE William Shakespeare, they didn't record his birth. Instead, they recorded his baptism on April 26, 1564. (Traditionally baptisms were recorded within a few days of birth, we think, so April 23 isn't a bad guess, but it's a guess, still.)
I think Shakespeareans and others just think it's easier to remember one date than to consider the complexity of remembering several.
But remembering that no one recorded his birth as such reminds us that much of life is up to chance, and that no one knows what's to come. And that's just as well, eh?
Complexity makes us think harder.