The owner of this site has taken it upon himself to digitize thousands of images of newspaper microfilms from New York Newspapers. The search function is clumsy and difficult to use, but the wealth of content here is amazing.
The Hathitrust Digital Library has thousands of digitized books that are now out of copyright. These are all full text searchable. Easy to use and an excellent resource for a scholar doing historical research.
The Google News Archive has access to citations and full text of historic newpapers going back to the 19th century. Included are citations to the New York Times. NOTE: For access to the New York Times Online you need to be on site in the library and have a librarian log you on.
The website provides a fully searchable index of websites that offer access to historical collections in digital format. Includes access to various types of media and content, including video, pictures and audio files.