The Mormon church does not support polygamy. In fact, the official church policy is that those who are found to be practicing polygamy lose their membership within the church.
Though church founder Joseph Smith was thought to have had as many as 50 wives, polygamy hasn't been a tenet of the Mormon church since the 1890s. Even when polygamy was an approved part of the Mormon faith, it is estimated that very few families actually practiced it, due to the high standards and many stipulations that were placed on doing so. For instance, the first wife had to grant permission for her husband to take additional wives. Faced with national anti-polygamy laws, the Mormon church was forced to abandon polygamy in the late 19th century in order to establish and maintain good relations with those around them.
The confusion about the status of polygamy in the Mormon church is likely due to some small polygamist sects that associate themselves with the Mormon church. The church insists, however, that these sects are in no way connected with the church and are living in strict violation of church law. Although the Mormon church no longer practices plural marriage, it does claim that the Bible does support it and that, at certain times throughout history, God has commanded men to take more than one wife.