Can Mormons use birth control?

Yes. As long as we're talking about pregnancy prevention, and not pregnancy termination.

Do they?

Sometimes it seems like we don't. When someone has learned how many children I have, their first question is often one of three: Are you Catholic? Are you a Pastor? Are you Mormon? Usually the people that ask these questions have a certain tone of admiration or respect, and I am flattered by it. Catholicism and some of the more fundamental forms of the protestant tradition are known for a long-standing prohibition on contraceptives, and many people associate Mormons with the older or more conservative side of Christian Culture. I think we should be pleased by that association.

Children are an heritage of the Lord. That's pretty much all the Bible has to say on the subject. The LDS Church doesn't publish much more than that, other than to recommend that decisions regarding 'family planning' be made prayerfully, involve husband and wife, and where difficulties arise, that they consult with their ecclesiastical leader (usually a Bishop or a Stake President) on the matter.

Quite basically, contraception is not to be used selfishly. There is an expectation that if you have the ability to bring children in to the world and raise them, you ought to do that. We encourage our members to obtain good education, good jobs, and self-sufficiency, as a means to that end. At the same time, we discourage our members from waiting until the 'perfect time' to have children. There is no perfect time. Children always mean sacrifice. But the church does not dictate a schedule, a quota, or otherwise interfere in a husband and wife's decisions.

The medical advances that permit things like contraception are, in my opinion, a blessing from God, not to be used selfishly, but to be used in prolonging life and improving its quality. So when a woman's mental/emotional/physical health is stressed, using those blessings under guidance from the spirit is entirely appropriate.

My wife and family are the highest priority in my life, after God. They come before my church callings, before my work, before even the worthiest of my hobbies.

Every now and then I have to check and make sure that the amount of time I am dedicating to those other things are appropriately balanced against family, and that my family is benefiting from my service in those areas. My service in the church has afforded me the double benefit of training in being a father. And I think if I didn't have a family, I wouldn't need a job, and I'd probably have quit my job a long time ago and gone and lived in the woods.

Let me make clear here: I have had many children because I love my children. Every one of them has increased the amount of joy that I have. When I was younger, my plans were not to have many. I only learned after having children how fulfilling it is. The church did not 'make me' have this many children. It was my choice, and I stand by it.

Now here's the fun part:

The other questions I get about my familial head count are often less flattering: Don't you understand how this happened? What are you putting your poor wife through? How is the world going to feed all of these children? Don't you worry about the environment/overpopulation/college costs/etc?

To those people I say (when I feel polite), my children are bright and well-raised and smart and caring, and are part of the solution to the world's problems, not part of the problem. I have some less-polite answers that call their own qualifications as parents in to question, but some (unwanted) maturity and wisdom I am picking up as I age are limiting that sort of conversation. My siblings (who are similarly prolific, but I am still winning in sheer numbers) have cute answers to these questions too.

Having children has a funny way of wiping the window through which you view the world. So let me air one final point: Your opinion on when to have children, how many to have, and so on, applies to just one person: You. And it barely even counts there.

Your right to weigh in on anyone else's life choices, whether to the extreme of too many or too few children, is limited by the fact that such a right does not exist.

Of course, you are free to moan and groan about the costs others may or may not impose on you through welfare or social costs. But, dear older-sister-whomever-you-are in the Relief Society of the Utah 457th Ward, if you think the newly married couple in your ward should have started having children already, you may (kindly) shut up and keep your opinions to yourself. And, captain-sierra-club-thomas-malthus-crusader, if you think I/we/someothercouple have too many kids and we're burdening the world, well, you may also (kindly) kiss off and find someone else to whine at. And, on a closing note, to the unmarried / no children yet intellectual who has figured out all the answers... good luck with that.