Oh, someone already mentioned Redguard.
Hm...
A lot of examples are really just "not white" which I don't think is what the OP is after but there are some good examples here. OP, I'm assuming you'd prefer playable characters but will settle for non-playable protagonist as well, right?
There's Urban Chaos for the PS1 which features a dark-skinned lady as the playable protagonist but I've heard it's not that good. (I've never played it, I just remember seeing it in a promo leaflet inside a Tomb Raider game when I was a kid and thinking she looked really cool.)
Valerie Blaylock from Trauma Centre:New Blood for the Wii is a playable black lady doctor. She's pretty badass to boot.
There's Nilin from Remember Me, of course.
Shinobu is a side-character assassin from No More Heroes 2 and there's Vivienne from Dragon Age Inquisition, also as a side character. Possibly Fran from Final Fantasy XII but since she's a rabbit...person...thing I don't know if she'd count.
I'm trying to name playable characters but sadly I don't think I can name any more and ironically I don't know any playable male black protagonists. I think, Gear of War maybe? (These types of shooters aren't my thing so I don't pay attention).