Alexander Hamilton was ineligible to be US President as he was born in the West Indies. Same reason Kissinger, Albright couldn't be president.
Also Ben Franklin, Bob Hope, and Arnold Schwarzenegger.
It did not apply to the founding fathers. There was an amendment to the effect that you had to have lived in the U.S. for x-years to become president if you were born before 1776.
Actually its even simpler. You needed to be a citizen at the time the consitution was adopted, if you were not a citizen by birth.
http://en.wikipedia.org/wiki/President_of_the_United_States#Requirements_to_hold_office