Beginning March 28th, the new digital subscription plan of the online edition of New York Times will limit public access of free contents to 20 articles per month. The law library has access (via Yale University Library’s subscription) to digital contents of the NYT from online aggregators such as Gale but the closest online alternative to NYTimes.com is the New York Times Image Edition provided by Newsbank. See earlier post here. Archives from 2007 are searchable and images of individual page or section can be printed but not downloaded. Online full-text contents of NY Times in HTML format provided by Gale start from 1985, by Westlaw and Lexis from 1980.
Another useful online newspaper aggregator is Proquest PressDisplay which includes image editions of close to 1000 domestic and foreign newspapers. Coverage varies depending on each newspaper. Back files of Chicago Tribune are available for the past couple of days but that of Le Monde are available for the past couple of months. To find available newspapers, search in Online Newspapers and Journals list by the title of the newspaper.