The Lutheran Church Missouri Synod, the most conservative of the major Lutheran denominations in the U.S., doesn't have an official position on contraception, but a 1981 report on sexuality by the Synod's Commission on Theology and Church Relations was "commended to the Synod for study and guidance" by the Synod in 1983. The report contained the following statement:
In view of the Biblical command and the blessing to "be fruitful and multiply," it is to be expected that marriage will not ordinarily be voluntarily childless. But, in the absence of Scriptural prohibition, there need be no objection to contraception within a marital union which is, as a whole, fruitful. Moreover, once we grant the appropriateness of contraception, we will also recognize that sterilization may under some circumstances be an acceptable form of contraception. Because of its relatively permanent nature, sterilization is perhaps less desirable than less-far reaching forms of contraception. However, there should be no moral objection to it, especially for couples who already have children and who now seek to devote themselves to the rearing of those children, for those who have been advised by a physician that the birth of another child would be hazardous to the health of the mother, or for those who for reasons of age, physical disability, or illness are not able to care for additional children. Indeed, there may be special circumstances which would persuade a Christian husband and wife that it would be more responsible and helpful to all concerned, under God, not to have children. Whatever the particular circumstances, Christians dare not take lightly decisions in this area of their life together. They should examine their motives thoroughly and honestly and take care lest their decisions be informed by a desire merely to satisfy selfish interests.
With respect to voluntary childlessness in general, we should say that while there may be special reasons which would persuade a Christian husband and wife to limit the size of their family, they should remember at all times how easy it is for them simply to permit their union to turn inward and refuse to take up the task of sharing in God's creative activity. Certainly Christians will not give as a reason for childlessness the sorry state of the world and the fear of bringing a child into such a world. We are not to forget the natural promise embedded in the fruitfulness of marriage. To bear and rear children can be done, finally, as an act of faith and hope in God who has promised to supply us with all that we "need to support this body and life."
This is pretty close to the view expressed by Albert Mohler, president of Southern Baptist Theological Seminary.
And it seems to me that the reasons cited here for the use of contraception are very nearly the same as those that Catholics cite as grave reasons for using Natural Family Planning to avoid conception while having sex.