Modern canon law of the Latin Church (a faction that keeps faith with the papacy) states:
Clerics are obliged to observe perfect and perpetual continence for the sake of the kingdom of heaven and therefore are bound to celibacy which is a special gift of God by which sacred ministers can adhere more easily to Christ with an undivided heart and are able to dedicate themselves more freely to the service of God and humanity.
There are deacons who never intend to take priestly vows who are not bound by this rule, but if they are married and their spouse dies, they are not allowed to remarry.
The Roman Catholic Church states:
All the ordained ministers of the Latin Church, with the exception of permanent deacons, are normally chosen from among men of faith who live a celibate life and who intend to remain celibate "for the sake of the kingdom of heaven." Called to consecrate themselves with undivided heart to the Lord and to "the affairs of the Lord", they give themselves entirely to God and to men. Celibacy is a sign of this new life to the service of which the Church's minister is consecrated; accepted with a joyous heart celibacy radiantly proclaims the Reign of God.
But acknowledges that this is not the case for everyone:
In the Eastern Churches a different discipline has been in force for many centuries: while bishops are chosen solely from among celibates, married men can be ordained as deacons and priests. ... Moreover, priestly celibacy is held in great honor in the Eastern Churches and many priests have freely chosen it for the sake of the Kingdom of God.
Curiously, these rules are not religious dogma; they are understood to be choices imposed by the hierarchy, and therefore are subject to change if authorities pursue that option. Anglicanism, Lutheranism, and Protestantism do not require that their ministers be celibate.
The apostles of Jesus were not required to be unmarried. Matthew 8:14-15 tells us "when Jesus was come into Peter's house, he saw his [Peter's] wife's mother laid, and sick of a fever." So Peter had a mother-in-law. Clement of Alexandria (c.150 - c.215 CE) claimed that Peter and Philip had children. Paul the Apostle, on the other hand, contrasts himself with other apostles by pointing out that some had wives while Paul had never been married. Paul clearly thinks his status is "better" when he write in 1 Corinthians 7:5-8:
Do not deprive one another except perhaps by agreement for a set time, to devote yourselves to prayer, and then come together again, so that Satan may not tempt you because of your lack of self-control. This I say by way of concession, not of command. I wish that all were as I myself am. But each has a particular gift from God, one having one kind and another a different kind. To the unmarried and the widows I say that it is well for them to remain unmarried as I am. But if they are not practicing self-control, they should marry. For it is better to marry than to be aflame with passion.
So you can better devote yourself to God if you do not have a woman around seems to be his attitude. Later in that chapter he expresses that an unmarried man can focus on God, but the married man has to deal with worldly things. The 3rd-century Manichaeans (whose enemy was Augustine) saw sex as corruption, as did the Montanists, whom Pope Innocent I tried to quash.
The first person to declare widely—and who had the power to enforce—that all marriages of priests were null and void and the children of such unions were illegitimate was not a pope, but a married man. Let's see who that was tomorrow.
