I am not saying that he isn't American, I am just saying that it is a legitimate question to ask if he is really a natural born citizen. He was born with dual-citizenship to the UK and the US, and then became a legal citizen of Kenya after it became an independent country. This is due to his father who was never legally recognized as an American citizen.
This is significant because if we use the definition of natural born citizen established by Emerich de Vattel in his The Law of Nations (a book known to have been read by Benjamin Franklin and George Washington, among other early US politicians) then we see that Obama is actually not a natural citizen, which is a constitutional requirement to be president of the US. Since the term "natural citizen" is never explicitly defined in the constitution, we cannot actually know for sure what the founders meant by it, but it is not a stretch to consider that they had Vattel's definition in mind.
The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for, if he is born there of a foreigner, it will be only the place of his birth, and not his country.Emerich de Vattel
Obama's supporters are quick to accuse anyone bringing this up as being racist but this has nothing to do with race - it is a matter of interpreting the laws established by the founders.