Are sportspeople okay? I was thinking of Nicky Winmar, Anthony Mundine and Cathy Freeman (all Australian Aboriginal).
Doctor Who has Martha Jones.
30 Rock has Tracy Jordan, Grizz & DotCom, Toofer and Elyssa.
Ugly Betty also has Renee, Hilda, Ignacio, Justin, Sofia.
Movie The Cider House Rules has Erykah Badu.
Stupid, Stupid Man has Anne.
Of course, anything Bollywood has Indians in it :D
There is a British police drama called The Bill which has had quite a few characters of colour; black, Indian, probably other. But I haven't watched it in ages so I'm afraid I'd be writing about characters from 2006!