Jews value life over just about all things. The life of the mother is valued, as is the life of the fetus. That said, different rabbis follow different teachings on when life begins. The majority of rabbis (Orthodox through Reform) see the fetus as a potential life, whose (potential) life is valued but not yet as valued as the actual (full) life of the mother. So the answer to the question of whether or not abortion is permitted is — it depends on the situation.
If the mother’s life is in danger, abortion is permitted — actually required, at any stage before the actual birth is fully underway and the baby has partially emerged.
Even among the most traditional communities, there are different rulings as to what constitutes “danger” to the mother’s life. More lenient Orthodox rabbis include psychological/emotional risks as included in reasons to permit abortion. Less lenient Orthodox rabbis say only actual mortal danger counts, or at the very least, serious physical illness. Many Orthodox rabbis permit abortion in cases where continuing the pregnancy would lead to less serious physical illness (diabetes or other debilitating illnesses) to the mother, or life-threatening diseases to the baby (e.g. Tay-Sachs).