This of course would rule out Obama, whose father was Kenyan (and, at the time of Obama's birth, a British subject), without the need to make him produce his birth certificate. Unfortunately from the teabaggers' point of view the same objection could be made retrospectively about Spiro Agnew, whose father was a Greek citizen at the time of his birth. There's also the intriguing question of whether people who were born in territories that only later became part of the US proper - such as presidential candidate Barry Goldwater, born in Arizona Territory - can count as "natural born citizens". If not, then I suppose the earliest date a candidate from the State of Hawaii would have been eligible to run for president would have been 1994, when the first cohort of natural-born citizens would have turned 35. That does seem a long time to wait on the off-chance that anyone born before 1959 might set about restoring the House of Kamehameha.
Anyhow, Wiki has a nice article on the controversies and rulings about the phrase "natural born citizen", and its various twists and turns. What it boils down to is that no one really knows, and that most authorities resort to citing other people who also don't really know but lived longer ago. (This is the essence of English case law.) In the light of this uncertainty I feel free to offer my own reading, which is that the Founding Fathers, fearful lest any amongst them should be tempted to follow Julius Caesar in setting himself up as sole ruler, intended to forbid anyone born by Caesarian section from running for the presidency. This is surely the most obvious construction of the phrase "natural born", especially in an age far too modest to include the word "vaginally" in its key political documents.
I realise that this interpretation won't be universally accepted, at least not straight away. Also, it will be up to the courts to determine whether citizens born by in vitro fertilization, surrogacy and other methods unknown to the Founding Fathers are eligible to run for president: that is the way law evolves. But in the meantime I call on all future candidates to declare exactly how they were conceived and delivered (preferably with photographic evidence). The people have a right to know.