US passports do include the bearer's date of birth. The date of birth is located on the data page of the US passport, on the upper right-hand side. The date of birth is also embossed into the passport's gold-colored seal, which is located on the data page as well.
The passport book includes your name, US citizenship, date of birth, photo, and signature. The date of birth is an important part of your US passport and it is used to verify your identity. When you travel outside of the United States, the US Department of State uses your date of birth to verify your identity and issue you a new passport. If you have a US passport, be sure to keep it up to date so that you can continue to travel freely.