If we're talking about two consenting adults having sex, they both bear a responsibility to the child. The child is the innocent party in all this who did not get to choose who his or her parents were going to be. We all know that condoms break and birth control pills sometimes don't work, and while both of those things reduce the chances of pregnancy, we all know that they are not 100%, and any act of sex could result in a pregnancy. This is why I personally believe that sex should only occur in a committed relationship where both parties are open to having children. If that's not the case, a man should go into the situation understanding that he doesn't get to tell a woman to have an abortion and that if he's going to have sex he better be prepared at the absolute minimum to feed, clothe, and shelter any child that results from such a sexual union. Furthermore, we as a society should hold him responsible for doing so, and stop having this double standard where women need to "be careful" while men can just run away from our responsibilities. Sex is a reproductive act. If you don't want children, and aren't willing to accept the inherent risk of having sex, don't perform reproductive acts.
Maybe we should handle it like car insurance. You can't go into a singles bar/join Match.com/etc., etc. unless you can show proof of Daddy insurance or Mommy insurance as the case may be. If you have an "accident" because you were drinking, you get your license to have sex taken away (maybe you get a big ugly stamp on your forehead and an ankle monitor or something). A "hit and run" (have sex with her and then disappear before she wakes up) will get you jail time if you've impregnated her, followed by fines and restitution. Maybe that would make the most sense if people are going to continue to have sex in non-committed relationships.