The New York Times just launched NYTimes.com Academic passes, which provide full access for 24 hours to the digital newspaper. You must have a Stanford email address to participate and there is a limit of 500 simultaneous users. The 24 hours begin at the time of claiming the pass and also allow access on most devices** to the NYTimes apps.
See the FAQ (pdf) for more information.
** Mobile apps are not supported on all devices. Does not include e-reader editions, Premium Crosswords or The New York Times Crosswords apps.
Please also see How do I find The New York Times online? for other means of access.