Newspapers have an immense amount of long tail content, but most of them don't have a clue that their old content is valuable. I'm excited to see that the Times is starting offer API's to let developers play with some of that long tail content.
The movie reviews API is really just a start. They also have a tags API, and they say that they're working on a search API on this page: http://developer.nytimes.com/docs/timestags_api
Newspapers, have read about a few sometime ago. Associated Press offers one (feeds).
But the best choice would be to go for Daylife's API. http://developer.daylife.com
They index news sources including blogs and newspapers and other sites. You can refine the sources by the sourceIDs and hence select only newspapers for your API results.
A sample Nytimes API can look as simple as this - http://nytimes.enterpriseapi.daylife.com/articles/obama
Vineet at daylife dot com
(although theirs seems to have no published APIs or documentation that I can find, yet)
Give me a news API and then we'll talk, NYTimes.
It's coming. I took the above quote from here: http://developer.nytimes.com/docs/timestags_api