In the May 1980 Ensign, LDS apostle David B. Haight spoke of Leo Tolstoy calling Mormonism the American religion. Elder Haight then said that Mormonism is "the greatest power in the world."

http://classic.lds.org/ldsorg/v/index.jsp?hideNav=1&locale=0&sourceId=0106615b01a6b010VgnVCM1000004d82620a____&vgnextoid=2354fccf2b7db010VgnVCM1000004d82620aRCRD

Here is a very brief and incomplete review of the ugly side of Mormonism in America.

1856
The Willie and Martin handcart disaster was the single largest disaster in the western expansion of the United States.

1857
The Mountain Meadows Massacre was the greatest massacre of Americans by Americans in the United States until the Oklahoma City bombing in 1995. Mormons initially blamed the MMM on the Paiutes.

1863
The Bear River Massacre was the single largest massacre of Native Americans west of the Mississippi. U.S. Army Col. Connor said this about the Indians: "mostly well armed with rifles, and having plenty of ammunition, which rumor says they received from the inhabitants of this Territory in exchange for the property of massacred [non-LDS] emigrants."

1950s to 1980
The Indian termination policy was pushed through by individuals who were members of the LDS church. Over half of Utah's Paiute died between the 1950s and 1980 as a result of it. The termination policy was declared wrong by United States President's Nixon and Reagan.

1994
Meyers v. Board of Education was a Utah case. It brought a U.S. Supreme Court ruling for Native Americans in public education that was the "Brown v. Board of Education" of Indian Country.

2008
Proposition 8.

2009
The Blanding Utah artifact raid was the nation's largest investigation of archaeological and cultural artifact theft in the history of the United States.
http://www.bia.gov/idc/groups/public/documents/text/idc-000940.pdf

What Tolstoy actually said, as referred by Haight, was:

"Count Leo Tolstoy, Russian author and statesman, in conversation with Andrew D. White, United States foreign minister to Russia, in 1892 said, “I wish you would tell me about your American religion.”

“We have no state church in America,” replied Dr. White.

“I know that, but what about your American religion?”

Dr. White explained to Tolstoy that in America each person is free to belong to the particular church in which he is interested.

Tolstoy impatiently replied: “I know all of this, but I want to know about the American religion. … The church to which I refer originated in America and is commonly known as the Mormon Church. What can you tell me of the teachings of the Mormons?”

Dr. White said, “I know very little concerning them.”

Then Count Leo Tolstoy rebuked the ambassador. “Dr. White, I am greatly surprised and disappointed that a man of your great learning and position should be so ignorant on this important subject. Their principles teach the people not only of heaven and its attendant glories, but how to live so that their social and economic relations with each other are placed on a sound basis. If the people follow the teachings of this church, nothing can stop their progress—it will be limitless.”

Tolstoy continued, “There have been great movements started in the past but they have died or been modified before they reached maturity. If Mormonism is able to endure, unmodified, until it reaches the third and fourth generation, it is destined to become the greatest power the world has ever known” (see Improvement Era, Feb. 1939, p. 94)."

It would seem that Tolstoy in 1892 was not very well informed about the Mormon church.