We really don't know for sure but traditionally, he was born 53 years before hijra (around 570) in the month of Rabi' al-awwal. Generally, Sunni Muslims consider today(12th of Rabi' al-awwall) to be Mohammad's birthday and Shia Muslims celebrate his birthday on 17th of Rabi' al-awwal. It is said that he was born in the year of the elephant (Am-ul-fil) or the year that Abraha attacked Mecca with war elephants.
Also, keep in mind that the Islamic calendar is not the same calendar that was used before the the establishment of Islamic caliphate. The previous calendars were probably lunisolar instead of lunar and the tradition of intercalation was also practiced. All of this makes it impossible to determine the certain date of Mohammad's birthday.

In addition to /u/vestayekta's comment it's worth noting just how historiographically questionable the sources are that assert things like his being born in "the year of the elephant" or that "Abraha attacked Mecca with war elephants."

This kind of information comes from the exegesis of the Quran in which these events are alluded to but not stated (interpretations of Sura al-Fil is the basis for the account of the "year of the elephant": http://quran.com/105, and good luck finding confirmation of the events described from the text itself) or else from the Sira (the prophetic biography which also includes details like angels assisting in battle and other miraculous and historically questionable occurrences) or the hadith which are subject to enormous academic skepticism.

Barring the discovery that pre-Islamic Arabs kept birth certificates we're just not going to be able to know this. Also worth noting that it's incredibly common to not reliably know the dates of birth for historical figures in this era. Death dates are more common.