Polygamy was only necessary as a means to allow for the church to care for all of the widows who resulted from the persecution of the Church. As men died off, more women had to be taken care of per man. When this was no longer necessary, the practice of polygamy ended.

But because a man can be sealed to more than one woman in his lifetime (thought not at the same time) A man can have multiple wives in the Celestial Kingdom for all time. Is this not correct?

On 8-17-2010, Tyler wrote: 
"First I believe the practice of polygamy was inspired during the difficult trek across the Plains" 
Actually LDS polygamy started during the time of Joseph Smith, as early as 1831 according to the summary of Doctrine and Covenants 132. This would have been more than a decade before the Saints' trek across the plains. 
 
Tyler also wrote: 
"where several widows needed to be sheltered and provided for."  
This gives the impression that "several" or even only a few men practiced plural marriage. It's true that not all men practiced this (they couldn't, think about the math), but a significant proportion of Mormon men practiced polygamy. Another error in this is the assumption that in order to take care of widows, it was necessary for these widows to be married. This has never been true in our U.S. society. In addition, though some of these plural wives were widows, many (most) had never been married before. On the other end of the spectrum, some of the plural wives were married to other men while being a plural wife to others.  
 
Tyler also wrote: 
"When the Saints arrived in the Salt Lake Valley and Utah the practice of polygamy was not as critical for the safety and security of the church".  
Polygamy did not provide safety and security for the Church. It brought persecution and violence to the Saints. It was a major factor in the assassination of Joseph Smith. 
 
Tyler also wrote: 
"Joseph Smith received the 12 Articles of Faith that requires the members of the church to obey, honor, and sustain the law". 
Polygamy was against the law from the beginning. And I believe another poster already mentioned that since the plural wives after a first wife were not legally married to the polygamous husband, they were legally committing adultery, which was also against the law. The 12 Articles of Faith had nothing to do with the end of polygamy.

On 3-24-2011, Mike Mormon wrote: 
"Polygamy was only necessary as a means to allow for the church to care for all of the widows who resulted from the persecution of the Church. As men died off, more women had to be taken care of per man. When this was no longer necessary, the practice of polygamy ended." 
Please refer to the census data. There were more Mormon men than women during at least most of the LDS polygamy era.

It has been stated more than once in this thread that polygamy was practiced as a means to care for a surplus of single and widowed women. This is a common misconception.  
 
Polygamy was practiced because it was a commandment of God. It was practice3d righteously by less than 15% of the men in the church and the average polygamist household included 2 to 4 wives. It was very rare for a man to have 10 or 20 or more as did Brigham Young and Joseph Smith.  
 
Another stumbling block (which has not yet been brought up in this thread) are several statements by Brigham Young indicating that he believed polygamy to be requisite for the Celestial Kingdom. Brigham no doubt did believe this and, for him, it was requisite. His statements, his belief, and that requirement do not pertain to us. He wasn't wrong. He just wasn't talking to us.  
 
Wilford Woodruff's explanation of his vision has already been explained here. In 1890 the first Official Declaration was published and the Church stopped (for the most part) the practice of polygamy.  
 
The enemies of the church weren't satisfied with "no new polygamous marriages" and insisted that all the current polygamous relationships be dissolved. Many (both husbands and wives) were jailed, some went into hiding, others sought refuge outside the reach of the United States.  
 
In 1904 the second Official Declaration was published promising the excommunication of any further participants in polygamous marriages.  
 
The reasons for polygamy are open for speculation but it must be remembered that it is merely speculation. God has not yet explained his reasoning. The reasons for the discontinuation were made clear. As a result of that and other concessions on the part of the Mormons (women had the right to vote in Utah. Mormons gave that up to conform with the rest of the nation) Utah was granted statehood. 
 
The doctrine of the church has remained constant; the primary doctrine being obedience to the Lord. Our understanding of that doctrine changes over time. So, too, does the direction given by the Lord.