Since 1985, a number of surveys (first by the Times-Mirror Corporation and later by Pew) have asked "How would you rate the believability of _____ on this scale of 1 to 4?" The scale goes from 4 ("believe all or most of what they say" to 1 ("believe nothing"). I picked four publications: the Wall Street Journal, USA Today, Time Magazine, and the New York Times, and summarized the results by the logarithm of positive (3 or 4) divided by negative (1 or 2).*
The obvious point is that ratings of the believability of all have declined. Two other points that I'm not sure of, but are interesting possibilities:
1. In 1985, the Wall Street Journal and Time were rated much higher than USA Today. In the last ten years, there's been little difference among them--that is, the ones that started higher declined faster (unfortunately they didn't ask about the New York Times until 2004).
2. The decline is pretty well approximated by a linear trend. However, it also seems like there was an additional fall between 2002 and 2004 from which they haven't recovered. It seems reasonable that some people would have felt they were misled after the Iraq war didn't go as smoothly as promised--and even though government officials were the original source of the misleading information, it the "believability" of news outlets would suffer.
*In retrospect, I should have just taken the averages on the four point scale, but for reasons that I have forgotten I started by collapsing the scores into two groups.