The answer, as is so often the case with statistical evaluations, is: It depends.
The average age of death of our past presidents is 70.9, which certainly doesn't seem too far from what we might expect of a normal person. In his 1998 book "The Mortal Presidency," political science professor Robert Gilbert estimated that it was actually a bit low. Presidents (excluding Reagan, who hadn't died yet) lived an average of 3.4 years less than other Americans born at the same time. If you take out those who were assassinated -- which, clearly, is a hazard of the job -- that drops to 2.1 years.
In his 2011 analysis, S. Jay Olshansky of the University of Illinois estimated that presidents lived longer than others in their age brackets -- or, at least, outlived one physician's estimate that presidents aged twice as fast during their terms in office.
The discrepancy rides on a few things. There's no question that presidents outlived the life expectancy from birth of other white men their age. (The one non-white male president, of course, is still alive.) When George Washington was born, the life expectancy of newborns was just over 30 years. Presidents have historically enjoyed the sorts of advantages that correlate to longer lifespans: education, income and so on. But it also depends on the reliability of the data. Olshansky combined available U.S. data with a set of life-expectancy data from France, because of the iffiness of the domestic data. Gilbert used data from the Census Bureau and the Commerce Department. Determining old life expectancies is surprisingly tricky, as even a cursory look at this NIH report makes clear. And, therefore, drawing clear conclusions about how much longer presidents might live is tricky, too.
There's a key point worth making here: The longer someone lives, the older they're expected to live. The average life expectancy of someone who is 20 in 2015 is necessarily lower than someone who is 70 in 2015, by virtue of the fact that many of the 20-year-olds won't make it to 70, dropping the average. So we took the age of the president at inauguration, rounded it to the nearest decade, and compared it to how much longer someone that age would be expected to live from the closest decennial to the inauguration. (See all of the points at which estimations come into play?) Under that calculation, 22 presidents died younger than might be expected, by an average of about 11 years. (They're in red, or black if they died in office, below.) Seventeen outperformed their peers, by 7.7 years. (They're in blue.)
On average, we got a 2.8 year difference between presidents and non-presidents, with the latter living longer. If you take out those who died in office, 17 lived longer than their peers and 15 lived shorter lives, by an average of 8.6 years. The overall average: Presidents live 0.1 years shorter, which is close to the 0.3 year difference Olshansky saw when he excluded the age-twice-as-fast factor. So: It's a wash. Half lived longer, half lived shorter, and the difference was almost zero.
Which would suggest, then, that presidents live about as long as anyone else. There's a lot of gray area here, we admit with alacrity. But there doesn't seem to be much evidence that presidents -- and we've only had a few dozen, mind you! -- live substantially shorter lives (barring tragedy) or substantially longer lives than anyone else. So if that was keeping you from running for office, sleep easy.