Wikipedia Summary (on 1/21/11): Missouri Executive Order 44, also known as the "Mormon Extermination Order" in Latter Day Saint history, was an executive order issued on October 27, 1838 by Missouri governor Lilburn Boggs. The order was in response to what Boggs termed "open and avowed defiance of the laws, and of having made war upon the people of this State…the Mormons must be treated as enemies, and must be exterminated or driven from the State if necessary for the public peace—their outrages are beyond all description." The order was formally rescinded in 1976.
What proceeded the Mormon Extermination Order was a speech given by Mormon Leader Sidney Rigdon on July 4, 1838. In that speech, it was Rigdon who first used the term 'extermination' and threatened to exterminate the non-Mormons.
Sidney Rigdon's July 4th Oration:
We take God and all the holy angels to witness this day that we warn all men in the name of Jesus Christ, to come on us no more forever. The men or the set of men that attempts it does so at the expense of their lives. And the mob that comes on us to disturb us, it shall be between us and them a war of extermination, for we will follow them till the last drop of blood is spilled, or else they will have to exterminate us; for we will carry the seat of war to their own houses and their own families, and one part or the other shall be utterly destroyed. Remember it then, all men! No man shall be at liberty to come in our streets, to threaten us with mobs, for if he does he shall atone for it before he leaves the place; neither shall he be at liberty to vilify or slander any of us, for suffer it we will not in this place. We therefore take all men to record this day, as did our fathers, and we pledge this day to one another our fortunes and our sacred honours to be delivered from the persecutions which we have had to endure for the last nine years, or nearly that. Neither will we indulge any man or set of men in instituting vexatious LAW-SUITS against us, to cheat us out of our just rights; if they attempt it we say woe be unto them. We this day, then, proclaim ourselves FREE, with a purpose and a determination that can never be broken. No, never! No, never!! No, never!!!"
Brigham Young blamed the extermination on fellow Mormon leader Sidney Rigdon:
"Elder Rigdon was the PRIME CAUSE OF OUR TROUBLES IN MISSOURI, by his Fourth of July oration."
(Times and Seasons, p. 667, 1838) Reference
More: To read the full record of events leading up to the Extermination Order, visit wikipedia