Is there a daily updated list of ships calling to/sailing from New York Port?

Hello Tavi-ga,

The Maritime Association of the Port of NY/NJ offer's realtime
ship/vessel traffic information for  vessel traffic. To access the
information however, you have to have a subscription.
You can read more about them and subscription information here.
http://nymaritime.servehttp.com/
http://nymaritime.org/mapony/joining.html

The World Ship Society has some information and a yearly schedule of
some of the ship traffic in the Port of New York. You can access that
information here.
http://www.worldshipny.com/
http://www.worldshipny.com/2004nycarrdep.html

If this answer requires further explanation, please request
clarification before rating it, and I'll be happy to look into this
further.
Nenna-GA
Google Answers Researcher

The lloyds registry provides that kind of information however it is not free