Before the 1980s, the LDS Church was generally more outspoken about it's teachings on birth control. A typical description, from books that compared the practices of various religions, was that the LDS Church advocates the rearing of large families so birth control was contrary to its teachings.
Some leaders perhaps overstepped their authority and said that contraception should not be used. There was a general feeling that by using birth control you were preventing spirit children, that you were destined to have, from being born into your family. Some members still feel that way.
“There is one thing that I am told is practiced to some extent among us, and I say to you that where it is practiced and not thoroughly repented of the curse of God will follow it. I refer to the practice of preventing the birth of children. I want to lift my voice in solemn warning against this, and I say to you that the woman who practices such devilish arts, or the man who consents to them, will be cursed of God. Such persons will be cursed in their bodies, cursed in their minds, cursed in their property, cursed in their offspring. God will wipe them out from the midst of this people and nation. Remember it. Mothers, teach this to your daughters, for I tell you it is true. I need not pronounce any curse, whatever my authority may be, but I say to you that women who take this course, and men who consent to it, will be cursed of God Almighty, and it will rest upon them until their generation shall be blotted out, and their name shall be lost from the midst of the Saints of God, unless, as I have said, there is deep, thorough and heartfelt repentance.” (Apostle George Q. Cannon, Collected Discourses, v. 5, October 7, 1894)
“The world teaches birth control. Tragically, many of our sisters subscribe to its pills and practices when they could easily provide earthly tabernacles for more of our Father's children. We know that every spirit assigned to this earth will come, whether through us or someone else. There are couples in the Church who think they are getting along just fine with their limited families but who will someday suffer the pains of remorse when they meet the spirits that might have been part of their posterity.” (Prophet Ezra Taft Benson, Conference Report, April 1969, p. 12)
“It is contradictory to this covenant to prevent the birth of children if the parents are in good health.
“Thirty-five years ago when I first started practicing medicine, it was a rare thing for a married woman to seek advice about how she could keep from having babies. When I finished practicing medicine, it was a rare thing, except for some faithful Latter-day Saint women, for a married woman to want to have more than one or two children, and some did not want any children. We in the Church must not be caught up in the false doctrines of the world that would cause us to break sacred temple covenants.” (Seventy J. Ballard Washington, April 1995 General Conference)
However, the current position of the church on birth control, according to it's website of gospel topics is the following:
Children are one of the greatest blessings in life, and their birth into loving and nurturing families is central to God's purposes for humanity. When husband and wife are physically able, they have the privilege and responsibility to bring children into the world and to nurture them. The decision of how many children to have and when to have them is a private matter for the husband and wife.
From pg. 167 of the CHI (2010) section 17.3.16 (emphasis added)
"The Church strongly discourages surgical sterilization as an elective form of birth control. Surgical sterilization should be considered only if (1) medical conditions seriously jeopardize life or health or (2) birth defects or serious trauma have rendered a person mentally incompetent and not responsible for his or her actions. Such conditions must be determined by competent medical judgment and in accordance with law. Even then, the persons responsible for this decision should consult with each other and with their bishop and should receive divine confirmation of their decision through prayer."
Reference: Gospel Topics: Birth Control