There exists two different Archieves;
The Full-text articles from The New York Times (1851-1980) in pdf format.
The webpage direction is: http://query.nytimes.com/search/query?1851-1980
And The Full-text articles from The New York Times (1981- ).
the main problem is that although it is free, plenty of the articles must be paid for been seen.
The webpage direction is: http://query.nytimes.com/search/query?