According to this survey done by The University Of Missouri Reynold's Journalism Course, the BBC was the fourth most trusted source of news.

1st The Economist
2nd 'Public TV'
3rd Reuters
4th BBC
5th US NPR
6th US PBS


This is from the Marketwatch web-site, here:-

"The results were based on a survey of more than 8,000 people conducted by 28 media organizations in the U.S. Participation was voluntary but respondents tended to reside near the news outlets that made the questionnaire available on their websites, and leaned toward the liberal side of the political spectrum."