You can go back through time in the NYT TimesMachine, which contains content from from 1851 through 2002*, and allows you to flip through the pages in their original look and feel.
*Please remember that, because of certain copyright restrictions, access to archived articles within the date range 1923-1980 is limited. Within this date range, you may only open 5 PDF articles per day. Also, content beyond 2002 may be added on an annual basis.
You can also access archival material using the NYT online search function:
And from the results list, you can choose to view content as html by clicking on the title link, or you can view it as it was originally printed in the TimesMachine: