JOEL - The Church of Jesus Christ has issued the following statement on this subject:

"While the First Presidency and the Quorum of the Twelve Apostles have not taken a position at this time on the newly emerging field of stem cell research, it merits cautious scrutiny. The proclaimed potential to provide cures or treatments for many serious diseases needs careful and continuing study by conscientious, qualified investigators. As with any emerging new technology, there are concerns that must be addressed. Scientific and religious viewpoints both demand that strict moral and ethical guidelines be followed." (9 August 2001)

So as you can see, they are sort of taking a cautious "wait and see" attitude on the subject while the field continues to emerge and they have had more time to study the benefits and consequences of the technology. I have an extensive background in the sciences and believe that stem cell research, if conducted under strict moral and ethical guidelines, has a great potential to help us find cures to many diseases and conditions that afflict man today.
Of course the main dilemma that is at the root of the controversy over stem cell research, is the same one that affects the abortion debate. At what point does life begin?
A safe and logical answer to the question is that life begins at conception, for that is the moment that the potential for the development of a new life begins. This is what the Catholics believe and because of this, oppose embryonic stem cell research. However, during the cloning process the egg, with its nucleus removed, is never fertilized with sperm, hence no conception has taken place. The LDS doctrine teaches that life begins at conception, but a living soul begins at the moment the spirit enters the body, which could happen any time after conception. One can argue that the spirit probably does not enter the developing embryo until it has at least implanted itself in the mothers womb. It is not uncommon for an embryo to fail to implant itself, so it would therefore be illogical for the spirit to have already united with it before that happens. During this time between conception and implantation, embryos can not yet be considered as individualized human life, since they still possess the potential to combine, or split, or fail to implant themselves in the woman's uterus.
Those that are for embryonic stem cell research argue that in vitro fertilization clinics routinely create more embryos than they implant in a mother's uterus, and they destroy the extras. If they are going to be destroyed anyway, why not put them to good use instead? The ones they do use are usually stored in a frozen state, later thawed and then successfully implanted in a mother's womb. Has the spirit already entered an embryo that is being stored at -70 C? I don't think so. But this is only my opinion.
Senator Hatch from Utah argues that, according to several University of Utah doctors, "allowing research with such cells could lead to breakthroughs against cancer, Alzheimer's disease, diabetes and heart disease. To me a frozen embryo is more akin to a frozen unfertilized egg or frozen sperm than to a fetus naturally developing in the body of a mother. I have searched my conscience. I just cannot equate a child living in the womb, with moving toes and fingers and a beating heart, with an embryo in a freezer." (Salt Lake Tribune 19 Jul 01).