As of 2014, polygamy, the act of having multiple spouses at a time, is not legal anywhere in the United States. According to the New York Times, the Supreme Court approved of each state's right to restrict polygamy as a form of marriage in 1879.
In 2014, the famous polygamous Brown family in Utah, from the television show Sister Wives, fought in court for the ability to live together without prosecution. They won their case and are granted protection from being persecuted in the state of Utah. The successful case did not grant them the ability to have multiple marriage licenses, and thus they are not considered technically polygamous by law.