Strongly negative — only for genuine villains or scandals. Compare the antonym
名扬天下 (míngyáng-tiānxià, "famous throughout the land"), which is purely positive, and
闻名遐迩 (wénmíngxiá'ěr, "known both far and near"), which is neutral-positive. Don't use
臭名远扬 sarcastically about a famous person you respect.