As part of the College Readership Program, Swarthmore students, faculty, and staff can access an unlimited number of NYT articles for free.
Sign up once: Create an account for the New York Times Academic Pass program. Your pass will expire after one year and then you can sign up again.
From the Tripod record linked above, you can chose current or archive access:
To access current articles:
To view the archives (1851 up to four years ago):