I've been meaning to dig in and take a stab at this myself, but via the Curt Jester I see that Aggie Catholics has asked a statistics professor to take a quick look over the study that the Guttmacher institute recently released on world-wide abortion. (Abstract here, full text by subscription to The Lancet only.)
The Guttmacher institute (the research arm of Planned Parenthood) releases one of these studies every few of years: the last one was in 1999 I believe. Each year a couple of specific angles are taken with the press. This year one of these is the claim that countries with legal abortion do not necessarily have higher abortion rates than those where abortion is illegal, but that abortions are far less safe in countries where it is illegal.
The professor points out a number of good methodological questions. At a more broad level, one of the things that struck me even in looking at the popular articles I've seen on the study is that since this is a country-to-country comparison, and primarily looks just at legality and frequency, it ignores a number of other factors. (For instance, the US has less legal restriction on abortion than Western Europe, yet twice the abortion rate. Africa is estimated, and there are some very big questions about their estimation methods, to have twice the rate of the US, despite abortion mostly being illegal there. And yet countries like China and Vietnam in Asia have twice the abortion rate of Africa, despite the fact that abortion is legal there.)
So yes, abortion rates vary a great deal as a result of factors other than legality, but this does not in any sense mean that outlawing abortion has no effect.
But since Aggie Catholic's professor has spent time with the actual source study (while I just read what was in the NY Times and such) go read what he has to say.