With a Star Trek-style transporter, it might be possible to beam a baby from the womb of a woman who doesn't want it to a woman who does. That should satisfy both sides of the abortion debate and save some money on in vitro research. It might also make embryonic stem cells harder to get, which would put a bit of a damper on that debate too.
Mokalus of Borg
PS - Of course the solution is impractical as yet.
PPS - Since we don't have any transporters.