Question: Are rabbis required to marry or can they remain celibate?
Answer: My own inclination is that because marriage itself is a positive
commandment, historically the "Rabbi" or "Sage" would have been subject to the same rules. In Rabbinic literature - that is Talmudic literature - there are numerous statements endorsing marriage positively and at the same time commenting negatively on celibacy (TB 29 b; TB Yev. 62b, 63a;). Lastly, marriage was so important that if finances were at stake, one should sell a Sefer Torah in order to marry (Meg. 27a).
Further in Jewish law, the European gloss of R. Isserles on the Shulchan Arukh OH 581:1 states that only one who is married may lead the congregation in worship - note that this is the Hazzan/Shaliah Tzibbur and not the Rabbi whose function may only have been to teach.
How does that relate to Rabbis today? Most Rabbis marry. They marry for the companionship and children, but also in doing so they can better understand the dynamics of the family, which they are often called upon to counsel. Most Rabbis are fortunate enough to find an appropriate mate, even in this very complicated world.
This are becoming increasingly complicated as some Jewish movements have already begun to ordain gay and lesbian Rabbis, to perform gay and lesbian marriages and/or commitment ceremonies. With that reality, the unmarried Rabbi - male or female - may unfairly be stigmatized, which would be cruel and unfair.
Lastly, some have also suggested that if one were indeed gay or lesbian, did not advertise that reality and lived an entirely celibate life, it would not preclude them from ordination. That is, it is the homosexual behavior that is forbidden in the tradition, not a judgment upon the person who is homosexual.
I hope that this is helpful as we are currently in very unclear waters, and perhaps as we ultimately learn what the Torah meant and ultimately how homosexuality comes to be a personal situation, we will deal with it equitably.