And it came to pass that I beheld, after they had dwindled in unbelief they became a dark, and loathsome, and a filthy people, full of idleness and all manner of abominations. 1 Nephi 12:23
Nephi in the Book of Mormon is seeing a vision from an angel. He looks at a multitude of people and calls them dark (skinned?), evil, filthy and lazy. This causes some to wonder if its a racist statement.
Maybe dark means dark-hearted and filthy means sinful and idle means not doing anything to change their spiritual state. However, in a later verse, Nephi says:
And I beheld the Spirit of the Lord, that it was upon the Gentiles, and they did prosper and obtain the land for their inheritance; and I beheld that they were white, and exceedingly fair and beautiful, like unto my people before they were slain. 1 Nephi 13:15
The first group did not have God's spirit. The second group did. Many wonder why Joseph Smith chose words like white/black if he didn't want it interpretted as a racist statement (which wasn't a problem to the people in the 1860s).
Later, in 2 Nephi, Nephi speaks of his brothers who have been cursing him. God then strikes them with a curse. What is that?
And he had caused the cursing to come upon them, yea, even a sore cursing, because of their iniquity. For behold, they had hardened their hearts against him, that they had become like unto a flint; wherefore, as they were white, and exceedingly fair and delightsome, that they might not be enticing unto my people the Lord God did cause a skin of blackness to come upon them.
And thus saith the Lord God: I will cause that they shall be loathsome unto thy people, save they shall repent of their iniquities. 2 Nephi 5:21-22
It's pretty clear here that he's talking about a curse on their skin. The curse on them became black skin and because of it, they become "loathsome."
It's racist to say being white is to be pure and delightful and to be black is to be sinful and evil.
Troubling still are these statements from LDS leaders:
"You see some classes of the human family that are black, uncouth, uncomely, disagreeable and low in their habits, wild, and seemingly deprived of nearly all the blessings of the intelligence that is generally bestowed upon mankind. The first man that committed the odious crime of killing one of his brethren will be cursed the longest of any one of the children of Adam. Cain slew his brother. Cain might have been killed, and that would have put a termination to that line of human beings. This was not to be, and the Lord put a mark upon him, which is the flat nose and black skin. Trace mankind down to after the flood, and then another curse is pronounced upon the same race--that they should be the "servant of servants;" and they will be, until that curse is removed."
Brigham Young-President and second 'Prophet' of the Mormon Church, 1844-1877- Extract from Journal of Discourses
"Shall I tell you the law of God in regard to the African race? If the white man who belongs to the chosen seed mixes his blood with the seed of Cain, the penalty, under the law of God is death on the spot. This will always be so."
Mormon 'Prophet' and second President of the Church, Brigham Young, spoke in 1863 (Journal of Discourses, Vo. 10, p. 110)
"The Blacks are denied the Priesthood; under no circumstances can they hold this delegation of authority from the Almighty. The Negroes are not equal with other races where the receipt of certain blessings are concerned, particularly the priesthood and the temple blessings that flow there from, but this inequality is not of man's origin, it is the Lord's doings."
Bruce McKonkie, Mormon Doctrine, pp. 526-527
For more on this:
http://truthandgrace.com/Racism.html
http://carm.org/mormonism-and-the-negro