Generally speaking abortion is prohibited. Nonetheless, it is not considered "murder", and there are actually instances when it is permitted. A qualified Halachic authority would have to determine that on a case by case basis.

The Askmoses Answer:

This is a very complex question and cannot be answered easily. Let us begin by pointing out the debate in the world at large centers around the rights of the woman to have an abortion, as opposed to the rights of the baby to live.

Torah does not talk in the language of rights. It talks of commands and prohibitions, duties and obligations. It uses the language of responsibilities.

The difference between the two concepts is profound. Rights are what we are entitled to claim from the world. Responsibilities are what the world claims from us. Rights demand; responsibility contributes. Rights are what we think others should do for us. Responsibilities are what we think we should do for others. An ethic of responsibility is more active and altruistic than a politics of rights.¹

The entire abortion issue needs to be understood in light of the above. The rule of thumb in approaching this question is therefore “what are my responsibilities and obligations as laid out in the Torah and Rabbinic texts?”
In Jewish law the abortion issue is not couched in absolute yes/no terms. The issues are very complex and there are many variables and provisos – far too many to cover in this forum. This question is therefore best dealt with on a case-by-case basis, since no two circumstances are identical, and what may appear to be insignificant differences from one case to the next can change the entire ruling.

Torah does not talk in the language of rights. It talks of commands and prohibitions, duties and obligations. It uses the language of responsibilities

IN GENERAL
There is a broad consensus among Rabbinical authorities that abortion is generally prohibited. However, they disagree as to whether the prohibition is Biblical or Rabbinic in origin.²

As a general rule, abortion in Judaism is permitted only if there is a direct threat to the life of the mother by carrying the fetus to term or through the act of childbirth. In such a circumstance, the baby is regarded as “pursuing” the mother with the intent to kill her.³

Despite the classification of the fetus as a “pursuer,” once the baby's head or most of its body has been delivered, the baby's life is considered equal to the mother's, and one life does not take precedence over another, because it is considered as though mother and child are both pursuing each other.

WHERE THERE IS DANGER TO THE MOTHER
Where there is danger to the mother abortion is permitted even in far-advanced stages of pregnancy.⁴

All Rabbinic authorities agree that abortion is permitted when the fetus is the direct cause of the mother's life-threatening condition (e.g. due to toxemia, placenta previa). Many Rabbinic authorities rule that abortion is also permitted when the danger to the mother is indirect (i.e., from a disease unrelated to the pregnancy, such as heart disease, diabetes, kidney disease, or hypertension).⁵

However, a fetus may not be aborted to save the life of any other person whose life is not threatened by the fetus, such as use of fetal organs for transplant.

Some Rabbinic authorities also recognize psychiatric factors in evaluating the potential threat that the fetus poses to the mother. However, the danger posed by the fetus (whether physical or emotional) must be both probable and substantial to justify abortion.⁶  The degree of mental illness that must be present to justify termination of a pregnancy has been widely debated by Rabbinic scholars,⁷  without a clear consensus of opinion regarding the exact criteria for permitting abortion in such instances.⁸

However, several modern Rabbinical experts ruled that since pregnancy-induced and post-partum depressions are treatable, abortion is not warranted.¹⁰

BIRTH DEFECTS
According to the view that the prohibition of abortion is Biblical there is no justification for aborting a fetus. This ruling applies even if it is clearly known that the newborn will only live for a short period of time, may be constantly ill, will have no mental faculties, or will require more attention than the mother is able to give.

But according to the view that the prohibition of abortion is Rabbinical in origin it may be permitted to abort the fetus in certain cases (after consulting a proper Rabbinical authority).

The following conditions must however be fulfilled: a) it is absolutely certain that the fetus is suffering from a certain disease or defect, as opposed to a mere probability of such a defect. Such certainty can generally be obtained by ultrasound examination or amniotic fluid analysis; b) the defect or illness is fatal within a short period of time, as opposed to fetal abnormalities which may lead to an inferior quality of life but are not fatal.

Where an abortion is permissible, and a proper Rabbinic authority has been consulted, the mother should not feel guilt or despair, but should resolve to fulfill the mitzvah (commandment) of “be fruitful and multiply” by bringing another Jewish child into the world

Tay-Sachs disease leads to severe physical and mental retardation, blindness, convulsions and death at about 3 or 4 years of age. Some authorities allow abortion when detected in the earlier stages of pregnancy,¹¹  other forbid it.¹²

Down’s Syndrome is a genetic disease that results in some degree of physical and mental retardation, but is not fatal. Most Rabbis would forbid an abortion in such a case.

Anacephaly is a lethal defect of the brain with absence of most of the brain and part of the skull. If the baby is born alive, it usually dies within a few days. Even some Rabbis who maintain the view that abortion is a Biblical prohibition permit abortion of such a fetus.¹³

Pregnancy reduction – if multiple fetuses constitute a danger to the mother it is certainly permissible to abort some or all of them to save her life.¹⁴  If there is no danger to the mother, but danger to some of the fetuses, it is permissible to destroy some of them to save the others.¹⁵ In all cases of pregnancy reduction it is preferable to perform the pregnancy reduction before forty days into the pregnancy where possible.

In all cases, it is incumbent upon the mother to ponder the sanctity of life and what after-effects an unsanctioned abortion may have on her and her family’s mental and emotional health. Where an abortion is permissible, and a proper Rabbinic authority has been consulted, the mother should not feel guilt or despair, but should resolve to fulfill the Mitzvah (commandment) of “be fruitful and multiply” by bringing another Jewish child into the world.

You might find the following related articles of interest¹⁶:
http://www.jlaw.com/Articles/stemcellres.html
http://www.jlaw.com/Articles/preemb.html