Okay.
The Catholic Church is made up of twenty-three individual “Churches,” all eventually (there will probably be some kind of technicality argument but whatever) led by the Pope. There is one Western Catholic Church, what we call the Latin Church, and the Pope is the immediate leader of it. There are twenty-two Eastern Catholic Churches, and they are self-governing in a sense; however, they are still led by the Pope as well, and they are as equally Catholic as any Latin Catholic.
It is the tradition of the Latin Church to require priestly celibacy. It is the tradition of the Eastern Churches to allow their priests to marry I believe before they are ordained, and most of them do, but this is not required.
Now, your question obviously applies to the Latin Church. The requirement is by default for all priests of the Latin Church to be celibate. Celibacy is not a vow, it is a promise. Celibacy is the promise to not marry, which in turn prohibits sex. However, there are some small groups of priests within the Latin Church who are nevertheless permitted to marry. For example, sometimes Protestant ministers are allowed to become Catholic priests, especially those with a good quality theological education (ie not from some tiny no-name Bible college); and more often than not, they are already married, and so they obviously retain their marriages after they are ordained priests. Also, there have been for quite a few years now, something like 30, Anglican “priests” who are married who convert to Catholicism and then are ordained priests. This is being accelerated now that the Ordinariates are being established which allow Anglicans to convert en masse. These Protestant and Anglican convert priests who are married are of course allowed to have sex and children.
Clerical celibacy is a practice, not a doctrine or dogma. Eastern Catholic priests and Protestant converts prove this. It is an ancient and venerable practice and from what it looks like, it isn’t going anywhere, and rightly so. (I support it fully) However, it could go away. But I highly doubt it will.
***What you refer to as a vow, as I said, is only a promise. Only male and female religious take vows of chastity (not celibacy), among others. Chastity means no sex, celibacy means no marriage. Essentially, they mean the same thing in practice, since without sex one cannot marry and without marriage one cannot have sex, but celibacy and chastity go at the issue from different angles and the reasons are somewhat different and so the “tone” of the practice is different.
How is celibacy maintained? Through bishops, superiors and good candidates to the priesthood. It is quite stupid, if I say so myself, for society to judge celibacy. Celibacy is a 100% free choice and no one is forced to live a celibate life since no one is forced to become a priest. Celibacy is a fantastic way to live an extremely holy and sanctified life.
