The oldest record of a birthday celebrated in the Bible is that of an Egyptian Pharaoh at the time of the patriarch Joseph. One of the sons of Jacob, Joseph lived from around 1709 to 1599 B.C. and spent the majority of his life in Egypt. The account of this event is in Genesis 40.
Our birthday example begins with a baker and a butler who served Pharaoh. They were both prisoners for bringing the wrath of their ruler upon themselves. While languishing in prison they meet Joseph. A married woman had falsely thrown him into jail when her sexual advances were rejected.
One night, a few days before Pharaoh's birthday, both the baker and butler have strange dreams.
In the butler's dream, he sees a vine that has three branches. He describes the dream to Joseph and states that he held in his hand the cup of Pharaoh. With cup in hand, he then "took the grapes (from the vine) and squeezed them into the cup and gave it to him (Pharaoh)" (Genesis 40:11).
The baker then says to Joseph that he dreamt he had three baskets on top of his head. The top basket held Pharaoh's baked goods, where the birds were eating them (Genesis 40:16 - 17).
What the dreams would ultimately mean for the butler and baker, as was foretold by Joseph under God's inspiration, would come to fruition three days later on Pharaoh's birthday. The butler was given back his job serving the ruler, while the baker was hanged (Genesis 40:20 - 22).
Some people have reasoned that since a hanging occurred on a birthday that it therefore is wrong to celebrate the day of a person's birth. This is a 'guilt by association' argument that does not make much logical sense. While one person lost his life when Pharaoh commemorated his birth, another one gained their freedom! Not only that, but it was eventually through the butler that Joseph's life was ultimately spared!
Joseph, after he was saved, went on to save his entire family (the patriarchs of the twelve tribes of Israel) from famine in the land of Canaan (see Genesis 45 and 46)! Added up, what occurred because of a birthday would be a strong argument for keeping them since more good than bad happened on the day!
The only other mention in the Bible of a birthday is that of Herod Antipas (one of Herod the Great's sons). The account is in Matthew 14 and Mark 6.
Briefly, Herod had thrown John the Baptist in prison because of comments condemning his marriage to Herodias. Both Herod and his wife wanted to put John to death. Herodias and her daughter Salome, on the day of Herod's birthday celebration, conspired to trick him so that he would be forced to kill the Baptist.
Salome's dance so pleased Herod that he promised her anything (Mark 6:23). She requested John's head on a platter, a gross and evil request that was fulfilled.
Herod's birthday was incidental to the overall desire to get rid of John. Using John's death on the day Herod decided to throw a party to celebrate when he was born, as a reason to shun rejoicing over one's birth, is a fallacious "guilt by association" argument.
The Bible does not say it is a sin to celebrate a birthday. There simply is no teaching concerning these events one way or the other. There are no verses that state it is wrong to keep track of the passing years of one's life. It is acceptable for a family to rejoice at a patriarchal father reaching a great age, or hugging and loving a child, giving them a gift and congratulating them on their special day!