My solution is to open an "Incognito Window" in Google Chrome or a "Private Window" in Firefox. Since the New York Times paywall is cookie based, these two methods work because they block cookies in your browser and give you full access to the site. A super easy way to access an article of your choice with this method is to right click on the link and then choose "Open Link in Incognito Window" in Google Chrome. In Firefox, just right click on any link and choose "Open Link In New Private Window". From the new window you can now search and read the site to your heart's content.
If you're feeling guilty, it may help to click on an ad on the site from time to time...or just give in and plunk down the money for a subscription. Times are tough...but the New York Times is a good outfit and we want them to stay in business.