Mark Twain wrote about polygamy among the Mormons in Roughing It. I can’t find my copy to give you an exact quote but he said something to the effect that he was, personally, going to put an end to it, he had the youth and energy to do it – until he saw the Mormon women. They were such pathetic, ungainly, homely creatures that any man who would marry even one of them deserved to be called a saint, and we should all take our hats off to the man who would marry fifty.
He also wrote a humorous account of dining with Brigham Young and being watched carefully to ensure that he didn’t give any gift to a child. If he had attempted to do so he would have been forcibly restrained. The reason given was that if he had succeeded, all the rest of the children would also want one and supplying all his children with gifts would have bankrupted Brother Brigham.
As a card-carrying Mormon I have heard a lot of theories about why polygamy (technically, polygyny – polyandry was never permitted) was allowed in the early days of the Mormon Church. Most of them center around an alleged imbalance in numbers – there were a lot more women than men and these women had to be provided for somehow. Sort of a welfare system, I suppose. There was not, and has never been, an official pronouncement stating why the practice was allowed (not merely allowed, but encouraged), just that it was sanctioned by God. There is also a lot of confusion about how prevalent the practice actually was and how it worked (and how well it worked).
The practice was ended, of course, when the anti-polygamy laws passed by Congress were upheld by the Supreme Court. The Church was disenfranchised and all its properties siezed by the federal government. The Church leaders felt that destruction of the church organization was too high a price to pay for compliance and petitioned the Lord for relief, which was granted. Since that time the practice of polygamy has been grounds for excommunication from the Church. (Those who were already polygamously married were allowed to quietly continue, with the consent of the Church and the government, as long as polygamy was no longer advocated and no new polygamous marriages were authorized.)
Because the commandment to practice “plural marriage” was ended due to government pressure, there is a small faction within the Mormon community (not the Mormon church) who believe that God has not, in fact, rescinded the commandment and that the practice should continue. This is the source of the ongoing Utah (mostly) polygamists. The Mormon Church doesn’t sanction or permit this, but the practitioners usually claim authorization, either directly or through some secret sub-organization that only the most faithful (i.e., themselves) are allowed access to.
The general belief among the Latter-day Saints is that marriage is ordained of God and that He can control the way it is practiced. In practice this means that historically polygamy has been authorized on occasion, notably in the Old Testament. The prophet Samuel stated that David’s sin with Bathsheba was not polygamy but adultery (and the accompanying murder, of course). His other wives and concubines were not considered sinful. OTOH, polygamy is specifically mentioned as one of the sins that needed correction by one of the prophets in the Book of Mormon. So, as I stated earlier, the general belief is that polygamy is a sin when God says it’s a sin, and it’s not when He says it’s not. The tricky part is in finding a reliable source for what God says, and we Mormons believe we have that.