The New Oxford American Dictionary has a note about using Negro.
Since the Black Power movement of the 1960s, however, when the term black was favored as the term to express racial pride, Negro has dropped out of favor and now seems out of date or even offensive in both US and British English. The 2010 US Census questionnaire was criticized when it retained the racial designation Negro as an option (along with Black and African Am.). The Census Bureau defended its decision, citing the 2000 Census forms, on which more than 56,000 individuals handwrote "Negro" (even though it was already on the form). Apparenly, Negro continues to be the identity strongly preferred by some Americans.
The NOAD itself, in the definition of Negro, reports the word as dated, and often offensive.
About Black, the note the NOAD has is the following:
Black, designating Americans of African heritage, became the most widely used and accepted term in the 1960s and 1970s, replacing Negro. It is not usually capitalized: black Americans. Through the 1980s, the more formal African American replaced black in much usage, but both are now generally acceptable. Afro-American, first recorded in the 19th century and popular in the 1960s and 1970s, is now heard mostly in anthropological and cultural contexts.