I'd like to make a few secular/political contributions to this question. This answer probably should not qualify for the accepted answer, but I think it's worth adding here that there are some good scientific legal arguments against abortion, and it's not solely an issue of religion vs science.
iswas legal in the United States because of the 1973 Roe v Wade decision. The ruling in this case specifically declined to look at whether or not a fetus is a human life. The justices attempted to side-step that polarizing issue. They could not settle the question, and so dealt with the fetus as merely a "potential" human life. I believe they hoped this would assuage the religious side by still treating the unborn as something special, as well as the secular side by declining to rule that a fetus was fully human. Regardless of their intent, the court took that baseline and then weighed whether the mother's right to privacy can exceed a mere potential human's right to life and the interest of the state in protecting that potential life — thus giving in by default to the secular view — and finds, to a point, in favor of the mother. That point, which was originally very limited, has today been stretched to breaking.
If the court's view of a fetus is sound, then the current prevailing secular position on abortion absolutely makes sense. A women should, moral issues aside and purely from a legal standpoint, be able to do with her own body as she pleases. However, if this is wrong — if a fetus is its own separate human life form, and more than just human in potentia — then the opposite view absolutely makes sense, and most (not all!) abortions are nothing short of state-sanctioned murder. It's also worth noting that, ethics aside and based solely on the science of the time, the court's view of a fetus was not entirely without merit.
However, science has learned some things since 1973. I'm talking here, of course, about DNA. While DNA has been known since the 1800's, it wasn't until the 1950's that scientists really began to understand it.1 The forensic and legal worlds took a little longer to embrace this, and it wasn't until 1986 that DNA is first used in court to exonerate and 1987 for conviction2 — well after Roe v Wade.
Today, I think most would agree that no other physical property more than DNA absolutely and definitively distinguishes one individual from another. DNA is used in courts to distinguish and prove not only individuals, but also family relationships and, most significantly here, different species. If the situation were examined again today, a DNA sample from a fetus would undoubtedly show that fetal tissue is both distinct from the mother and also entirely human. While I have not, of course, had the opportunity to confirm this, it is my (admittedly limited) understanding of animal biology that a hypothetical DNA sample taken from a fetus would be a match for that of the adult, should the fetus continue to develop and ultimately reach that stage of life.
The significance here is that fetal tissue, having distinct human DNA, should probably no longer be considered as merely a part of the mother's body. Take religion out of the debate completely, and the science says that a fetus is both fully human and separate from the mother. A woman has the right to do with her own body what she wants... but now we have the rights of another individual involved as well. A woman has the right to do with her own body what she wants... but the scientific evidence shows that the fetus is more than just part of the mother's body.
Now we must take this new understanding of the scientific evidence into account, and use it to re-examine the current legal environment. Since an unborn fetus is a definitely a distinct human entity, as demonstrated by it's DNA, and more than a mere potential human as it was treated by Roe v Wade, we can say the current Supreme Court ruling is clearly inadequate. A new ruling must be established, and this can only be (re-)settled by the courts. But my opinion is that a much better legal interpretation of this new evidence would make use of same legal doctrine that allows the use of a murder victim's corpse for forensic purposes, even over the objections of next of kin. In this context, we can say that the unborn individual would likely want to live, and that the state has the power to compel the mother to allow this. Doubtless those in favor of legal abortions will come up with their own arguments, but as they have as yet largely declined to move beyond Roe v Wade, I haven't heard anything more compelling.
As a complete aside to the question, it boggles my mind that Pro-Life groups continue today to make religious arguments for their position against people who will only acknowledge arguments grounded in a framework of science, when there is a perfectly good scientific argument for the Pro-Life position ready and waiting. I agree with the religious argument as well, but as Levar Burton said, "You don't have to take my word for it.", when there is (to the Pro-Choice view) a more credible source at hand. I feel like pushing the DNA argument more strongly could change the conversation about the issue and tilt more opinions in the Pro-Life direction. I've heard it said by some on the Pro-Choice side that those who are Pro-Life hate women. Surely they understand that this argument reciprocates and, if true, by their own logic and arguments Pro-Choice groups hate children.
 History of DNA research (Wikipedia)
 DNA profiling (Wikipedia)