Jane Galt, a generally pro-choice libertarian sort, has a great essay about abortion and responsibility that parallels most of my own opinions on the matter.
If I don't use my birth control correctly--if I forget a pill, don't notice my patch has fallen off, use a petroleum-based lubricant that dissolves latex, or decide to go without a condom or my diaphragm "just this once"--am I responsible for the pregnancy that results? Damn straight.
If paying attention to really rather simple instructions, which are included right in the box, is truly beyond your abilities, then you need to be in a state home where you can be taken care of like the mental infant you are. This is not to say that everyone who has an accident is a mental infant--it seems like every third morning I forget either my asthma pills, or my inhaler, and yet I have my own apartment and student loans and everything. But if I have an asthma attack because of this, it's my own damn fault. I can't blame anyone else, or the universe, for something that I could easily have prevented with a little more care.
Given those rates, it seems safe to say that at least 80% of couples who got pregnant while "using" birth control are responsible for what happened to them.
Then, of course, there are the people who unintentionally got pregnant while not using birth control--although I don't see how you can call this "unintentional". It's rather like "unintentionally" getting fat while eating supersize McDonalds meals three times a day.
... I think that responsibility does matter. If you knowingly take a risk, and something happens, society rightfully does less to help you avoid those consequences than if you were just touched by the fickle finger of fate. And intuitively, people are, and I believe will remain, far more horrified by the woman who is on her fourth abortion because she just can't be bothered to use birth control consistently, than by that 1-in-200 woman who found out, the hard way, that she's one of those lucky few who just don't respond well to the pill.
The most offensive aspect of abortion is that many women use it as a form of birth control. Jane Galt has more thoughtful posts about abortion if you scroll through her archives towards the future.