John McCain (born 1936), who ran for the Republican party nomination in 2000 and was the Republican nominee in 2008, according to his birth certificate, was born of two U.S. citizen parents at Colon Hospital in Colon, Panama. The city of Colon was outside the US administered Canal Zone and remained Panamanian territory throughout the existence of the Panama Canal Zone.
Róger Calero (born 1969) was born in Nicaragua and ran as the Socialist Worker's Party presidential candidate in 2004 and 2008. In 2008, Calero appeared on the ballot in Delaware, Minnesota, New Jersey, New York and Vermont.
George Romney (1907–1995), who ran for the Republican party nomination in 1968, was born in Mexico to U.S. parents. Romney’s grandfather had emigrated to Mexico in 1886 with his three wives and children after Utah outlawed polygamy. Romney's monogamous parents retained their U.S. citizenship and returned to the United States with him in 1912. Romney never received Mexican citizenship, because the country's nationality laws had been restricted to jus-sanguinis statutes due to prevailing politics aimed against American settlers.
Running as a party's candidate and actually being voted in as US president are two different things.