There is a lot of confusion regarding polygamy and Mormons. The main reason for this confusion is that there are several Mormon religions.
When Joseph Smith was shot and killed in a Illinois jail cell in 1844 he left a power vacuum. There was no process in place for determining who would become the next leader of the church. A power struggle ensued. Some Mormons believed that the oldest son of Joseph Smith should become the new leader, others thought that this or that church elder should assume the leadership of the church. Eventually the largest group organized around Brigham Young--the leader who would take the Mormons to Utah.
This group became the largest of the Mormon religions, but that does not mean that the other groups have no legitimate right to the mormon title. Today the different factions that broke off after the death of Joseph Smith have formed into a number of different Mormon faiths. The group that followed Brigham Young became the Church of Jesus
christ of Latter Day Saints (or by their acronym LDS). They are currently one of the fastest growing religious groups in the world with about 14 million members worldwide, about half of which reside in the United States.
These Mormons, the LDS, think of themselves as the true Mormons and the other groups as apocryphal. The other groups are tiny by comparison.
The LDS Mormons do not practice polygamy. They were forced to abandon that practice by the United States government who sent the army to Utah to enforce the United States claim on that territory.
But several of the other Mormon offshoots still practice polygamy. These groups get all the press on this subject and therefore many people believe that all Mormons practice polygamy. The vast majority do not.
However there is another complication--the LDS Mormons still believe in polygamy in the afterlife. They believe that the Mormon men in the past who had multiple wives will remain married to those wives in the afterlife. Mormon widowers can take another wife and will then be married to both of those wives in the afterlife.
The last Mormon to have multiple wives in this life died in the 1950's. That is because there were still some polygamous marriages sanctioned by the church even after the LDS Mormons renounced bigamy.
At times in the past Mormon prophets (every Mormon head of the church is considered a living prophet who speaks directly to God) have stated that a man must have multiple wives to become a God. Mormons believe that all Mormons have the chance to become gods. The Mormon line on polygamy has changed radically throughout the history of the church.
Originally the Mormons denounced polygamy, but Joseph Smith was sexually involved with numerous girls and women--some were girls as young as fourteen. The church tried to cover this up but eventually it could not be contained any longer--there were simply too many accusations--and something had to be done. So Joseph Smith had a vision and God told him to take multiple wives.
He wrote out this vision on a piece of paper. It quoted God as addressing Joseph Smith's legal wife. God tells her that she will go to hell if she doesn't allow her husband to have multiple wives. Mrs. Smith was apparently a strong minded woman because she took this piece of paper, with the message directly dictated by God, and threw it in the fire.
Nevertheless Joseph convinced his wife to allow three of the other wives to move in with them. That was short lived and after a brief time the original Mrs. Smith threw them all out of the house.
Joseph Smith however continued with his spiritual wedding night consummations and it was probably the most important factor that led to his downfall because many Mormons were vehemently opposed to polygamy and saw it as an idication that Joseph Smith was a scoundrel. One of these men started a newspaper with the intent of denouncing Smith and detailing his peccadillos. Smith sent his militia to burn down the press offices. This got him arrested and he was shot by a mob while in jail awaiting trial.
Here is a video documentary I made of this text:
http://youtu.be/bsoV0hcuxNg