William Shakespeare died at the age of 52, on April 23, 1616. Based on the date of the Old Style, or Julian, calendar of his time. Based on the New Style, or Gregorian, calendar, the date is May 3, 1616. He was buried in the chancel of the Church of the Holy Trinity in Stratford, and his gravestone bears an epitaph supposedly written by Shakespeare himself. It warns:

Good friend for Jesus sake forbeare,
To dig the dust enclosed here.
Blessed be the man that spares these stones,
And cursed be he that moves my bones.

Well that's an interesting question, depending on who you think Shakespeare is!

That Shakespeare died on April 23, 1616, buried in Stratford at the same church in which he was baptised.
Whether or not he wrote the plays is an entirely different matter!