I haven't got a lot of time tonight to talk about this, but I'm very interested in discussions I've seen regarding Barack Obama's racial identity--particularly because the meanings of social category names is a major (though at the moment suspended) research interest of mine. On the Obama issue see, for example, this article and this one, both from salon.com. The first one claims that Obama is not really black in American terms, since he is not decended from American slaves.
Meanwhile, in the UK, Black History Month (in October, as opposed to February in the US), at least in my English town, is focused on "the history of Asian, African and African Caribbean peoples." Plainly, the use of black varies, at least around the edges, in the two countries. As in AmE, the primary BrE sense of black is 'person of sub-Saharan ancestry',* but AmE's main second sense tends to be restrictive (i.e. 'descendants of American slaves'), while BrE allows more inclusive interpretations.
But that's all I can afford (time-wise) to say at the moment, so I'll leave it at that and will promise more on black after one of my students finishes the research for his BA dissertation (AmE thesis) on the meaning of black in the UK today.
*And no, I'm not counting among 'persons of sub-Saharan ancestry' the Afrikaners or other people whose ancestors (somewhere between Lucy and grandma) are European. And yes, I am aware that most 'black' people in America have some European ancestry (the one-drop rule, and all that). As I said, I need to be brief!