OK, urbanlegends.about.com

The forwarded email asserts that because Obama’s Kenyan father wasn’t a U.S. citizen, and because his mother, who was a citizen, didn’t fulfill the supposed legal requirement of “resid[ing] in the United States for at least ten years, at least five of which had to be after the age of 16,” Obama himself was therefore not a citizen at birth.

That is false on two counts:

Obama was born on U.S. soil — in Honolulu, Hawaii — and was therefore a citizen at birth by virtue of the Fourteenth Amendment (and the principle of jus soli).
The stated residency requirement, in effect between 1952 and 1986, applied only to parents of individuals born outside the United States.
Therefore Barack Obama is, in fact, a U.S. citizen. But some still argue that he is not a natural-born citizen. The reasons have to do with the disputed meaning of the term “natural born” itself.

However, on assumption that Obama was not born on the US soil, the residency requirement kicks into place.

ranchodlaw.com

The rules changed again for people born between January 14, 1941, and December 23, 1952. When one parent was a citizen and the other a foreign national, the rules changed substantially. To pass on citizenship, the citizen parent must have resided in the U.S. for at least 10 years before the birth of the child, and at least five of those years had to be after the parent turned 16. Children born out of wedlock to a U.S. citizen mother who met the residence requirements were automatically citizens.

Obama’s mother would be too young to qualify. So if Obama were born outside of the US, he would not automatically get the citizenship (and certainly would not have been a natural born citizen). Which is why birfers are intent on proving that Obama was born in Kenya.

However, since Obama was born in the US, this fact makes all the stuff about the citizenship of his parents moot - he is a natural born citizen by jus soli.