Only native-born U.S. citizens (or those born abroad, but only to parents who were both citizens of the U.S.) may be president of the United States, though from time to time that requirement is called into question, most recently after Arnold Schwarzenegger, born in Austria, was elected governor of California, in 2003. The Constitution originally provided a small loophole to this provision: One needn't have been born in the United States but had to be a citizen at the time the Constitution was adopted. But, since that occurred in 1789, that ship has sailed.
Basically, you have to have been born in the United States, or been born abroad to US citizens. Also the person needs to be at least 35 years old and have lived in the US for 14 years (although it isn't clear whether this has to be consecutive or not).
*NOTE: Information obtained from usgovinfo.about.com.
SCJA
When I die, I want people to look at me and say "Yeah, he might have been crazy, but that was one zarkin frood that knew where his towel was."