Apparently the first of Barbie's black friends came out in 1967 and was called 'Colored Francie', but was withdrawn because of racial tensions at the time. The first African-American Barbie ("Black Barbie") followed 13 years later.
The inventors of Barbie, Mattel, originally created 'black Barbie' by simply filling the 'white Barbie' mould with dark plastic. But since then, they've atoned by developing "ethnically accurate head moulds" for their non-white dolls.
And finally (from Wikipedia):
In 1997, Mattel joined forces with Nabisco to launch a cross-promotion of Barbie with Oreo cookies. The toy producer introduced "Oreo Fun Barbie", marketed as the perfect after-school playmate, someone with whom little girls could play after class and share "America's favorite cookie". As had become the custom, Mattel manufactured both a white version and a black version.
Unfortunately for Mattel, its product developers were unaware that in the African-American community, Oreo has another meaning. It is a derogatory term for a person perceived to be, like the chocolate sandwich cookie, black on the outside and white on the inside - someone with an ambivalent racial identity, who does not identify with African American culture, or who is perceived as a "race traitor" or a self-loathing black person.
The black doll hit the market with a thud, production on it ceased, and Mattel quickly recalled all unsold stock.