In Firefox on Winders: Ctrl-Shift-P

In Chrome on Winders: Ctrl-Shift-N

In Safari on Winders: Click on the "Gear" at the upper-right, select "Private browsing..."

(Make the appropriate key substitutions for your OS of choice.)

Cookies will be sandboxed in such a session. You can go to the NY Times (and probably the Washington Post and others that have a free article limit) and browse to your heart's content. When you reach the limit, just close the Private session window and start it again - your count will go back to zero.

Alternatively, do a Google or Twitter or Facebook search of a quoted sentence from the article and you'll often get a clickable link to the full thing.

Of course, if you read scores of articles at such sites every week, you should feel guilty enough to have some sort of subscription. ;-)

HTH!

Cheers,
Scott.