I have a subscription to New York Times in order to get their daily and
Sunday crossword puzzles.  When I registered I opted out of receiving
e-mail announcements from them.  I have not seen any increase in junk
mail.

At the Agreement Page, http://www.nytimes.com/subscribe/help/agree.html
they state in part, the following:

8.  Communications between NYTEMC and subscribers

8.1  Unless you indicate on your registration form that you do not want
to receive such information, NYTEMC, its owners and assigns, reserve
the right to allow certain third party vendors to provide you with
information about products and services.

8.2  NYTEMC reserves the right to send electronic mail to you for the
purpose of informing you of changes or additions to the Service.

8.3  NYTEMC reserves the right to disclose information about your
usage and demographics, provided that it will not reveal your personal
identity in connection with the disclosure of such information.  For
more information please read the privacy statement of The New York
Times on the Web. [ http://www.nytimes.com/subscribe/help/privacy.html ]

You might consider using an alternate e-mail address just for NYT if
you're concerned.  You can safely ignore or reject all e-mails to that
ID.  But that might cost more or not be possible, depending upon you
service provider.

My provider, AOL, allows up to 5 ID's, each comes with Mb of storage
on their server (10 Mb total).  I use one ID <WWineburgh> to get all
e-mail, and the others only for storage of web page files -- they are
marked to reject all e-mail.

Bill Wineburgh