The Bible does not clearly address abortion. The closest the Bible gets to the topic of abortion is a law penalizing men who would hit a pregnant woman, causing her child to die (Exodus 21:22-23). Aside from that specific instance in the Bible of killing children inside of the mother's womb, there is mention of killing children once they have been born. And, that is abominable according to the Word of God.
The first noteworthy example in the Bible of infanticide is in the book of Exodus when Pharaoh orders for the murder of all newborn male children. It was such an abhorrent act that God commended the midwives for lying to save their newborn children. The act of infanticide is then reflected later on in the story of Jesus' birth where king Herod ordered for the death of every male child under the age of two years. The New Testament even cites a prophetic Scripture referencing Rachel weeping for her children. These two examples, however, are infanticide on a mass scale from an outside oppressor and not the decision of the parents.
In Deuteronomy 9:5, God says it is for wickedness' sake that he drove the Caananite nations out from before the Israelites. One of the chief sins among the Caananites was infant/child sacrifice where they would burn their children alive. This is very similar to the brutality involved in an abortion.
The case that is given to justify abortion today is made by liberal Democrats. They claim that it is in the name of women's rights that she may have an abortion if she so desires. It is also under the guise that the baby, in its mother's womb is nothing more than a mass of cells and is essentially part of the mother's body. This is not true.
Having taken courses in bioethics, I do not recall a single case where even the most liberal ethicists would say that an unborn child was not a living organism nor would they concede that it was not human. Every serious ethicist, that I studied, concluded that based off of scientific data the unborn child was both living and human. The argument that liberal ethicists make to defend a pro-abortion stance is that the child is not a contributing member of society, thus he or she is not a person. If you think that argument is absolutely absurd, you are correct.
It is a myth that killing an unborn child is in favor of women's rights. Pro-life advocates believe in women's rights, but they also believe in the rights of an unborn child. The woman has rights,the choice is made when two consenting adults decide to have intercourse, which may result in the conception of a child. Once a life is born, the right to harm that child is not a right. The baby has a right to live. If an unborn child is both living and human, it follows that he or she is not just a part of his or her mother. Baby is a distinct human being. Thus it is no longer a right for a woman to decide what to do with that child's life anymore than it is her right to murder a full grown adult.
There are, of course, objections to this argument. Without going to deep into the cases of rape and incest, I will simply state that a child should not be punished for the crime that another person committed against his or her mother. What about the case where a mother's life is at risk? Even in these cases, abortion is not necessary. A reliable OB will tell you that if worst comes to worst, a woman can be induced and prematurely deliver the baby to avoid an abortion. Even if the child dies in this instance, it at least gives them the possibility for life opposed to prematurely terminating the life.
As serious of an offense as abortion is, it is forgivable by God. Jesus died for the sins of all mankind and that includes those who have had an abortion. Where the Old Covenant would say such a person should be killed, the Gospel teaches that we can extend grace to people who have made a mistake like this. Sadly, most women consent to have abortions because they are misled into believing that their unborn child is just a mass of cells. My heart goes out to these people. I pray we now seek truth from the Word of God, rather than the ideas of sinful mankind.