Because Polygamy was outlawed by the U.S. Government.

Yes, the US Government did outlaw polygamy. But that wasn't the reason that the Church abandoned the Practice. The US Government outlawed it, and the Mormon Saints of the day were willing to lay down and die for their religious convictions. But they were under a lot of controversy under the subject which led the leaders of the church to go to the Lord in prayer and ask the Lord what they should do. The answer is recorded in an Official Declaration by the church. The Current Prophet at the Time (Wilford Woodruff) wrote: "The Lord showed me by vision and revelation exactly what would take place if we did not stop this practice. If we had not stopped it, you would have had no use for . . . any of the men in this temple at Logan; for all ordinances would be stopped throughout the land of Zion. Confusion would reign throughout Israel, and many men would be made prisoners. This trouble would have come upon the whole Church, and we should have been compelled to stop the practice. Now, the question is, whether it should be stopped in this manner, or in the way the Lord has manifested to us, and leave our Prophets and Apostles and fathers free men, and the temples in the hands of the people, so that the dead may be redeemed. A large number has already been delivered from the prison house in the spirit world by this people, and shall the work go on or stop? This is the question I lay before the Latter-day Saints. You have to judge for yourselves. I want you to answer it for yourselves. I shall not answer it; but I say to you that that is exactly the condition we as a people would have been in had we not taken the course we have.  
. . . I saw exactly what would come to pass if there was not something done. I have had this spirit upon me for a long time. But I want to say this: I should have let all the temples go out of our hands; I should have gone to prison myself, and let every other man go there, had not the God of heaven commanded me to do what I did do; and when the hour came that I was commanded to do that, it was all clear to me."

Phillip wrote on 01-23-2008 14:45 
 
"Yes, the US Government did outlaw polygamy." 
 
I think this may be a little misleading. As I understand it, Polygamy was always illegal in every state in which it was practiced. I believe it was illegal in Mexico and Canada as well. It's not that the U.S. government made polygamy illegal. There were new federal laws put into place to allow the feds to go after the polygamists. In addition, polygamist men were also committing adultery from a legal perspective. (I'm not arguing they were adulterers from a theological perspective. That's a much larger topic.) These new federal laws gave the government some teeth that could be used to cause a lot of trouble for the Church as Phillip indicated in his quote above. The Church stopped polygamy to avoid these harsh consequences.

I just wanted to add, Congress would not allow Utah to be annexed as a state unless the Utah state constitution would outlaw polygamy. Also, the US government was beginning to seize church property; but gave it back once polygamy was outlawed.

Why do we refer to it as polygamy?  
If you look at the definition of polygamy it is: “The practice or condition of having more than one spouse.” That would have me think that multiple Husbands can also be practiced. 
Should we not say Polygyny? “The practice or condition of having more than one wife at one time.” 
[/B]spousewife

First I believe the practice of polygamy was inspired during the difficult trek across the Plains where several widows needed to be sheltered and provided for. 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. That being said well before the debate about statehood the Prophet Joseph Smith received the 12 Articles of Faith that requires the members of the church to obey, honor, and sustain the law. So the answer that Wilford Woodruff received was also inline with the earlier revelation and we see that God is the same today as he is yesterday as he will be tomorrow. If the lord needs the members to practice polygamy again he will provide a way.

As Job stated, "the Lord giveth, and the Lord taketh away, blessed be the name of the Lord". The Lord commanded the saints to live this law and uphold it, even at the risk of their own lives. I doubt it had much to do with more women than men. From 1862 to 1890, the saints obeyed God rather than man. They were willing to sacrifice everything to obey his law. Many went to prison. President Taylor died in hiding. However, when the Lord revealed to his anointed that their sacrifice was enough, then the practice was discontinued. It is an everlasting principle (Doctrine & Covenants 132) that has been rescinded until further notice.

what influence did the mormon religion have on american society

does the church still believe that it is ok to take on more then one wife? or are the ones that do take on more then one wife excompuncated for this practice.

Polygamy was abandoned in the late 1800's. If someone were to do that now they would be excommunicated.