Science indicate that 1-4% of the genomes of Eurasians and Pacific Islanders contain DNA from Neanderthals, which Africans don't have. See John Hawks and Carl Zimmer. This suggests that shortly after human beings left Africa, about 50,000 years ago, they interbred with Neanderthals, who were then living in the Middle East, before spreading to the rest of the world. Specifically, they compared the genomes of people from France, China, New Guinea and Africa (Yoruba and San) with the genomes from the bones of several Neanderthals. Presumably, that suggests that all human beings living outside of Africa might have Neanderthal genes. Even if you're African American, you probably have Neanderthal DNA, since most blacks in America have some mixed ancestry, and even some Africans must also have Neanderthal genes, since there has always been some migration in and out of Africa. There's a caveat that it's still early days, and these are small sample sizes, and there are other possible explanations of the data, so the picture will become more refined in the future, but for now it looks pretty likely that most people outside Africa may be hybrids. It's also possible that we have genes from others, like Homo erectus; we're still finding more hominids.
Now I'm feeling offended by those GEICO commercials!
UPDATE: I just got the free MEanderthal iPhone app from the Smithsonion, so I'm adding this image of myself from the app, since it fits so perfectly with the title.