JOEL - There were actually blacks in the Church as early as 1830. However, The black population was relatively low for a long time because the Church did not actively proselyte in areas where the population was mostly black. That has changed now and the black population in the LDS Church is now growing quite rapidly, especially since the revelation in 1978 allowing blacks to receive the priesthood.
According to the Encyclopedia of Mormonism, "Following the 1978 priesthood revelation, proselytizing was expanded worldwide to include people of African descent. Between 1977 and 1987, Church membership grew from 3,969,000 to 6,440,000, an increase of 62 percent. Because LDS membership records do not identify race, it is impossible to measure accurately the growth of black membership, except in areas where people are largely or exclusively of African descent. In the Caribbean, excepting Puerto Rico, membership grew from 836 to 18,614 and in Brazil from 51,000 to 250,000 during that decade.
Excluding South Africa, where the membership was predominantly white, membership grew from 136 in 1977 to 14,347 in 1988, almost all in west Africa."

The first entirely black African stake was organized in 1988. There are some black leaders in the Church. Helvecio Martins, a black Brazilian businessman, baptized in 1972 became a general authority in 1990. Others have become Area authorities and mission presidents.

According to the scriptures Cain was cursed as a fugitive and a vagabond because of his deed in killing Abel. (Gen. 4: 11-15)
It is clear God marked Cain to set him apart from others that he be not slain for his deed. We know that the descendants of Cain were given a "mark", but we don't know that the "mark" that God gave Cain was the black skin. Exactly why the Blacks of African descent were given the black skin and were denied the priesthood for so long is something only God knows for sure. Some have conjectured that the spirits of the blacks were not as valiant in their support of Christ's plan in the pre-existance compared to others and were therefore denied priesthood blessings. But this is not supported by any scriptures. Besides, if this were the case, then there would be no expectation they they would ever receive the priesthood in this life, because it would be unfair to those who had been denied it up to that point.
Church leaders have explained that whatever the reason, the matter is confined to one of lineage. According to the Book of Abraham, the pharoahs of Egypt were to be denied the priesthood (Abr. 1:23-26), but it does not say why nor does it say for how long. It is interesting to note that black skinned people of other races have always been allowed to hold the priesthood in the LDS Church. These people were Aborigines from Australia, Fijians, Negritoes from the Philippines and Indians from India and Fiji whose skin can be blacker than that of some Africans.

It should also be noted that the Church has never rejected blacks for membership, unlike the vast majority of white protestant churches, nor has the Church ever segregated its black members from the white.
This is not the only time restrictions have been placed on who should and should not receive the full blessings of the Gospel. At the time of Moses, the Melchizedek Priesthood was taken from the children of Israel. In its stead they were given the Aaronic, or Lesser, Priesthood. This priesthood was restricted to worthy males of the tribe of Levi. During His ministry, Jesus instructed His twelve disciples that they were not to go to any of the Gentile nations or to the Samaritans to preach the Gospel, and that they were to go only to the lost sheep of the house of Israel (Matthew 10:5-6). Apparently, it is up to God to say when people are ready to receive the full blessings and responsibilities of the Gospel and when they are not.

Another thing to consider is that the Priesthood has never been held in bondage. Aaron and his sons weren't allowed to exercise the priesthood until after the children of Israel were free from Egypt. This was also the case when the nation of Israel was carried away into captivity in Babylon. Similarly, certain groups in modern society have been held in slavery as well. And even though this condition was not their fault, they could not be allowed command of the Priesthood until they were free as well. Even though the Civil War ended slavery, many things did not change culturally for the Blacks until efforts of the Civil Rights movements in the sixties and seventies. One might reason that by 1978 the Lord could see that the Blacks could finally regard themselves as being free from bondage, and were therefore given the Priesthood.

Also consider, that the LDS church has always taught(before and after 1978) that all children who die before the age of accountability(8 years) are saved in the highest kingdom of God(Celestial), regardless of race or color.

Church leaders of the past have always told us that someday everyone would be able to receive the full blessings of the priesthood and Temple ordinances. Even Brigham Young back in 1852 said, referring to blacks, that the "time will come when they will have the privilege of all we have the privilege of and more."
In 1947 President David O. McKay said, "Sometime in God's eternal plan, the Negro will be given the right to hold the priesthood. In the meantime, those of that race who receive a testimony of the Restored Gospel may have their family ties protected and other blessings made secure, for in the justice and mercy of the Lord they will possess all the blessings to which they are entitled in the eternal plan of Salvation and Exaltation."

When that time finally came and the revelation was collectively received by President Kimball and the 12 Apostles, Elder Bruce R. McKonkie explained, "And we all heard the same voice, received the same message, and became personal witnesses that the word received was the mind and will and voice of the Lord."

Here are some good sites about this topic on the Internet:
Black Mormons and the Priesthood Ban
The Genesis Group
Updated statement from the Church on Race and the Priesthood (2013)