A few days ago I realized that Barack Obama is the first person elected (or otherwise becoming) President who was born in what was, at the time of his election, the newest U.S. state (Hawaii). Check this list of Presidents and their birthplaces against this list of U.S. state admissions.
Now, it's been 49 years since the last new admission of a state, the longest such gap in history, so that makes that somewhat more probable now. Imagine if, say, Benjamin Harrison (actually born in Ohio) had been born in what was the newest state when he was elected in 1888, Colorado. Obviously it would have been impossible for him to have been born in a post-statehood Colorado, since that would have required him to have been 12 years old at the most. But more importantly, if we allow for him to have been as old as he was (born 1833) and born in territorial lands that later became Colorado, we would have to then consider that only about half of the state was U.S. territory at the time, and the part that was hadn't been settled by white people yet. So he would have either had to have been a Native American or the son of a mountain man's wife.
Not many Presidents have been frontiersmen; even Kentucky had already been a state for more than 18 years when Lincoln was born there. Checking the same references as above, we can see that Obama is also the first person elected (or becoming) President who was born in what was at the time of his birth the newest U.S. state. Additionally, since the country was established (i.e., since the States ceased to be British colonies), no U.S. President has been born in a territory rather than a state, even though it's perfectly legal. You'll recall that John McCain was born in the Panama Canal Zone, and the other Republican Senator from Arizona who unsuccessfully ran for President, Barry Goldwater, was born in a pre-statehood Arizona Territory. I don't know of any other territory-born Presidential also-rans, but I suppose I could do the research.
Here's some extra trivia for you: Obama is the only person elected President while the state of his birth was the current U.S. State Quarter design. In fact, the Hawaii quarter was released just the day before the election!