1. The one and only birthday mentioned in the Torah is that of Pharaoh! (Genesis 40, 20) Therefore there are opinions that celebrating a birthday is a non-Jewish thing and Jews should avoid it.
2. Another reason not to celebrate birthdays is according to the Talmud (Eruvin 13b) where there is a discussion if it was worthwhile that man was created or would it have been better had he not been created. The discussion concludes that it would have been better if he hadn’t been born. That’s why many use this source to say birthdays should not be celebrated. Others quote the continuation of that same Talmudic discussion that says “and now that he was created he should investigate his deeds”, meaning now that we are here we should on one hand take time for introspection and on the other hand celebrate our entry into the world to be able to keep G-d’s mitzvoth and good deeds.
3. Others say birthdays should be celebrated because of its importance in the life of man. In the Jerusalem Talmud (Rosh Hashanah ch.3 law 8) it brings down that “on ones birthday his mazal is strong and good.” His birthday and the day of the week influence a person’s life and his quality of life.
4. Our sages say that on a person’s birthday he receives an abundance of (spiritual) strength of life every year. In many places people make a small celebration just for the sake of celebrating. In Judaism however a birthday is a serious thing, it’s a day of reflection and reckoning. On this day that he came to the world is the best time for personal reflection asking himself: “Where did I get to up to now? What did I do with the strengths G-d gave me? Did I do good in my life or G-d forbid the opposite?”
5. In the Chabad “Book of Customs” it brings down “A person should sit alone and contemplate on his birthday remembering his deeds and those that need repair to repent and repair them.”
6. A person should do more good deeds on his birthday to increase good in the world. It’s proper to give charity on this day and if it’s a day the Torah is read, to get called up to the Torah. If it isn’t, he can get called up on the Shabbat before or after his birthday.
7. In Chabad Hassidut and in other circles, people recite the psalm with the number of their age daily. Someone 50 would say psalm 51 daily as he is entering his 51st year. On his birthday he starts the new psalm for that year.
8. Though we mentioned the dispute about celebrating birthdays it is unanimous that a 13 year old boy celebrates his bar mitzvah. It is a very important day when the boy enters the obligation of mitzvoth. This day id celebrated with a festive meal and of course the celbation of being able to do mitzvoth as the boy can join and be counted in a “minyan” quorum of 10 for prayers, and he gets called up to the Torah and he starts putting on tefillin.
9. The 60th birthday is considered special as someone who reaches 60 is considered having outlived a potential decree of being “cut off” and dying young as punishment for certain sins. People who are supposed to get “karet -cut off” may not live to age 60, so someone 60 celebrates not being “cut off”.
10. Some have the custom to fast on their birthday and others complete a tractate of the
Talmud on their birthday and celebrate with a mitzvah meal for the completion of the tractate.