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
This article gives an overview of the history of celibacy in the clergy. Even the Catholic church would admit that celibacy was not enforced on clergy in New Testament times, but would point out that those who chose celibacy were held in high honour, even in that period. There is dispute over how early the rules of celibacy came to be enforced. The earliest enactment of a rule was around 300AD at the Spanish Council of Elvira. This was not a universal rule. The rules appear to have been gradually tightened over the next few centuries,:


  [...] the synods of the sixth and seventh centuries, while fully recognizing the position of these former wives and according them even the formal designation of bishopess, priestess, deaconess, and subdeaconess (episcopissa, presbytera, diaconissa, subdiaconissa), laid down some very strict rules to guide their relations with their former husbands. 


Even centuries after that the practice was not universal.