Punchline = Polygamy
I realize that most of the people making these jokes probably know that Mormons (mainstream, not Fundamentalist) don't practice polygamy anymore, but I just can't help becoming aghast each and every time.
Of course, maybe I just see more of it than most people. I do watch a lot of Stand-Up, but the topic also hits mainstream in a lot of sitcoms and some dramas.
My husband recently learned much more about Mormons and the LDS faith through reading Under the Banner of Heaven by John Krakauer. Although much of it focuses on two Mormon Fundamentalists who committed murder "on God's orders" in 1984, Krakauer also gives an extensive history of the founding of the church. Apparently he gives information that is balanced with both the official LDS accounts and the "anti-Mormon" accounts. Since the book spent a number of weeks on the New York Times Best seller list in 2003, the concept of Mormons & polygamy spent some more time in the spotlight.
I sincerely doubt that the association between polygamy and Mormons will go away any time soon. I do wonder, however, if that would improve if polygamists were prosecuted, taking away the appearance of acceptance by the state government in Utah.