Polygamy: The Fundamental(ist)s (twop)
Sounds like this show will stir up controversy and questions. I thought I'd start a thread devoted to non-plot related religious discussion and questions.

HBO put the disclaimer up as favor to the LDS church. Here are some articles that show that the disclaimer itself is misleading:
Big Love's disclaimer needs a disclaimer
Big Love, September Dawn, and The Solomon Key (Big Love's disclaimer is discussed in the first third of the article.)

Here is the basic beliefnet.com entry on polygamy and the LDS church:
--The Mormon Church and Polygamy A quick history lesson in the Mormon church's involvement with the issue of plural marriages-- Mormon pioneers brought the practice with them during their 1847 exodus to the Great Basin. During the pioneer days, only about 20% to 25% of Mormon families were polygamous, according to the Encyclopedia of Mormonism. But the rest of the nation so opposed Mormon polygamy--Abraham Lincoln called the practice, along with slavery, "the twin relics of barbarism"--that the U.S. government refused to allow statehood for Utah unless the church gave it up. So (!) in 1890, Latter-day Saints President Wilford Woodruff announced a divine revelation (!) that the church was ceasing the practice. Although many LDS polygamists refused to abandon their plural wives and families at the time, since 1904 it has been Mormon church policy to excommunicate members who practice or openly advocate polygamy.

This is much more interesting. It's an FAQ written by a polygamist in Utah. I don't think the percentages are too accurate, but the perspective is fascinating. I had no idea what polyandry was and didn't know that the LDS church used to practice it. If you do read this, just keep the source in mind:

Mormon doctrine states that in order to enter the highest heaven that those who enter must be living in polygamy. Mormon doctrine also states that we believe in being subject to the laws of the land, insofar as those laws protect individual rights. So for the time being, the largest Mormon sect, the LDS church, has decided it is more important to live the laws of the land than those of God. Other Mormon faiths have made a different choice in the matter, and practice polygamy in defiance of the unjust laws of the land.
The LDS prophet John Taylor was visited by Joseph Smith and commanded to ordain apostles outside of the normal chain of command in the church, and commissioned them to carry on the practice of polygamy, even after the church abandoned it. So the practice continues among those who feel that it is more important to obey God than it is to obey the government. These folks are called Mormon Fundamentalists.
There are generally three major polygamist ideologies. One is represented by the folks of Colorado City, which takes a very conservative approach, saying that the purpose of intimacy is for procreation only. Another ideology which teaches that intimacy is to be enjoyed, is more typical of the AUB, Apostolic United Brethren. The third iealogy teaches that men and women as individuals are capable of making their own decisions in regards to lifestyle and belief, and that neither the church nor the state should interfere in family matters. These folks are sometimes referred to as Independent Mormon Fundamentalists.

Polygamy was lived secretly in the LDS church from about 1831 to 1852. The first mormon prophet had 20-30 wives and was murdered for practicing plural marriage privately while denying it publicly. (Smith? - was murdered? for reasons to do with his marriages?)
Polygamy was lived openly from 1852 to 1890 by the LDS church in Utah. The church made a show of abandoning the practice in order to get statehood. It wasn't until the second manifesto about 20 years later that the church started excommunicating new polygamists. Since that time, the LDS church has taken a very harsh and intolerant stance against anyone who publicly admits that they practice polygamy, or claims that it should be practiced.. (Polygamy still happens among members of the LDS church, just so long as those practicing in it are discrete, but not a moment longer.) nicely said.
It's not really the practice of polygamy that is punishable, but the flaunting of it to the rest of the world.
Based on the polygamists that I have known over the years, I estimate that about 3% of those you see in an LDS church on Sunday are practicing polygamy. Next time one of the brethren at a ward picnic introduces you to his sister, or his mother, or his aunt, who happens to live in his home, or introduces you to his single next door neighbor, you might wonder about what relationship they really have... It is very common for polygamists to rent or buy a duplex, and for the families to live side by side. It is an excellent way of being discrete.
The State of Utah could in theory prosecute someone for fornication or adultery, but since the anti-adultery laws are not enforced against the general population, polygamists cannot be singled out for prosecution.
Why is polygamy banned by the Utah constitution? The short answer is because the people of Utah were coerced by the Federal government.
The laws vary from state to state, but in general, if you do not ask for a marriage license from the state for your first (marriage), then you can cohabit with as many people as you like and it is not illegal.
Bigamy and Adultery are only crimes for a married person, not for people who are living together. Some jurisdictions have laws against having unmarried sex, but they are never enforced.
The largest concentrations of Polygamists in Utah are near Manti and in Hillsdale (Colorado City, Arizona). Practically the whole town of Colorado City is owned by a religious trust, the members of which practice polygamy. Wherever the LDS has a large concentration of Utah born members, you can be sure that there is polygamy close by.

See Also:
Women Want Polygamy - Curse of Monogamy - Letters about Polygamy - Utah Laws about Polygamy - LDS (Mormon) Church on Polygamy