Here's what I found. Let me know if I missed any.
Mary (Jesus's mother) was exceedingly fair and white.
And it came to pass that I looked and beheld the great city of Jerusalem, and also other cities. And I beheld the city of Nazareth; and in the city of Nazareth I beheld a virgin, and she was exceedingly fair and white. 1 Nephi 11:13Jesus, of course, was as white as his mom, as were his disciples. Indeed, after they were blessed by Jesus, the disciples became whiter than anything else on earth -- as white as Jesus even!
It came to pass that Jesus blessed them as they did pray unto him; and his countenance did smile upon them, and the light of his countenance did shine upon them, and behold they were as white as the countenance and also the garments of Jesus; and behold the whiteness thereof did exceed all the whiteness, yea, even there could be nothing upon earth so white as the whiteness thereof. 3 Nephi 19:25
And when Jesus had spoken these words he came again unto his disciples; and behold they did pray steadfastly, without ceasing, unto him; and he did smile upon them again; and behold they were white, even as Jesus. 3 Nephi 19:30The Nephites (God's favorite people) were also white and exceedingly delightsome.
It came to pass that the people of Nephi did wax strong, and did multiply exceedingly fast, and became an exceedingly fair and delightsome people. 4 Nephi 10Even the Gentiles (white, non-Mormon Protestants in Mormon-speak) were exceedingly fair and beautiful.
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 13:15But the Lamanites (or Native Americans) were not. They were once "a delightsome people," but God made them a dark-skinned, "filthy and loathsome people, led about by Satan" because of their unbelief and idolatry.
This people ... shall become a dark, a filthy, and a loathsome people ... because of their unbelief and idolatry. ... They were once a delightsome people ... But now, behold, they are led about by Satan. Mormon 5:15-18Still, there is some hope for Native Americans. If they convert to Mormonism, their skins will turn white, and they will become a "delightsome." (The original "white" in this verse was later changed to "pure" to soften the obvious racism of this prophecy.)
And then shall they rejoice; for they shall know that it is a blessing unto them from the hand of God; and their scales of darkness shall begin to fall from their eyes; and many generations shall not pass away among them, save they shall be a pure and delightsome people. 2 Nephi 30:6It happened before. God removed his curse from the "good" Lamanites (the ones that "united with the Nephites"), and they "became exceedingly fair, with skins "white like unto the Nephites."
It came to pass that those Lamanites who had united with the Nephites were numbered among the Nephites; And their curse was taken from them, and their skin became white like unto the Nephites; And their young men and their daughters became exceedingly fair, and they were numbered among the Nephites. 3 Nephi 2:14And it can happen to you, too. If you turn to God and become Mormon, God will make your skin spotless, pure, fair, and white.
O then ye unbelieving, turn ye unto the Lord; cry mightily unto the Father in the name of Jesus, that perhaps ye may be found spotless, pure, fair, and white. Mormon 9:6So there you have it. According to the Book of Mormon, the whiter the skin, the closer to God.