Unfortunately, we do not know the precise date of William Shakespeare's birth. In Early Modern England, record keeping was not as rigorous as it is today. What's more, Shakespeare would not have been born in a hospital or birthing center setting where a birth certificate might have been issued. The good news is that most churches kept records of baptisms, weddings, funerals, and the like, and records from a church in Stratford-upon-Avon indicate that Shakespeare was baptized on the 26th of April, 1564.
At the time Shakespeare was born, there was no strict rule for when children were supposed to be baptized. Especially if a baby was born small or not expected to survive, parents might wait to have a baptism performed until they were certain that the child would survive. The traditional date given for Shakespeare's birth, which is unverifiable, is the 23rd of April-- three days prior to his baptism. A baptism at three days old would be sensible, giving the mother and baby enough time to rest and recover after the difficulties of labor. The number three is also very important in Christianity, so baptism on the third day of life may have been considered auspicious by Shakespeare's parents.