As far as the Romans go, for the most part they did not. In fact they opposed it quite harshly. During the first few centuries AD, they persecuted many Christians and Jews for living this practice. Many of the Romans seemed to have a hatred for the practice.
But years after Rome became tied to the Catholic Church, Emporer Valentinian I (321-375 A.D.) tried to legalize polygamy so that he could take as a second wife a young woman that he had become infatuated with. As an excuse, he brought to light the fact that some Christians were still living it in secret.
In 393 A.D., Emperor Theodosius issued a particular law against polygamy in an attempt to try and stop all of the Jews that were still openly living it within the Roman Empire.