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The New York Times website has details of where copies can be bought on microfilm and CD-ROM:
Sources for Full Text and Abstracts of the Times
Full Text
Complete Archive: an online database of every article published in the final Late Edition of the Times from June 1980 through the current day. Available from Lexis-Nexis.
CD-ROM: a cumulative CD-ROM disk of every article published in the final Late Edition of the Times; it is published monthly with the final disk containing a complete year. A backfile of annual disks back to 1981 is also available. Available from UMI and in libraries.
- Microfilm: every issue, page by page, since The Times began publishing in 1851; also available on microfiche since 1981. Available from UMI and in libraries.
Abstracts
Online: complete abstracts of the final Late Edition of the Times, fully indexed, from January 1969 to the present. Available from Lexis-Nexis.
Printed Index: The New York Times Index, a printed index to the final Late Edition with complete abstracts, is published twice monthly along with three quarterlies and one annual cumulation. A complete backfile dating from 1851 is also available. Available from UMI and in libraries.
Other than that, it will depend on where you are in the world. In the first instance, check with your local library.