To follow up on a previous post that touched on the church and vasectomies, I found this from the Bishop's Handbook. It's amazing what you can find online. (The picture is not from the handbook. Too bad. It would have been more entertaining.)
Surgical sterilization (including vasectomy)
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. Source: Handbook 2: Adminstering the Church
So. If one of you decides that someone needs to get neutered because you've got more kids than money and sanity, you gotta go ask the bishop. Of course, if having all those kids has caused a woman serious trauma and she is no longer responsible for her actions, it's okay. But then who takes care of all the existing kids? It's a conundrum, for sure.