When did the prohibition of marriage for priests in the Catholic church originate?

The Bible mentions that one of the miracles Jesus performed was the healing of Peter's mother-in-law. This makes it quite clear that Peter himself was married, and Peter is the considered the first Pope by Roman Catholics. I've also heard that many if not all of the first popes were married and had families. So, my question is this: When was it that marriage first became prohibited for priests and popes in the Catholic church (for Latin Rite priests)? > And immediately he left the synagogue and entered the house of > Simon and Andrew, with James and John. Now Simon’s mother-in-law lay > ill with a fever, and immediately they told him about her. Mark > 1:29-30 ESV