The New York State Archives was established in 1971. The physical archives are in Albany, New York, and they also have a Website.
The Archives are home to more then 200 million documents related to the history of New York State from the 1600s to the present. Needles to say, there is a tremendous amount of genealogical information to be found in these records. They have also partnered with Ancestry.com to provide free access to various New York State records (users will have to create a free account at Ancestry.com). See Ancestry.com New York.
The Document Showcase page is a feature that highlights specific topics and changes with time. It is accessible with a link from the Home page. The current topic is American Indians in Colonial New York. Among the digital documents that can be accessed is a 1644 declaration of Cornelis Cornelissen, Jan Hageman, and others testifying how the Indians set fire to and destroyed the house of Jochem Petersen Kuyter.
I have also used the Pathfinder Tool which is a very helpful guide on how to locate naturalization and probate records.
There is a lot to explore on this website including photographs, an online catalog for the e-Library and much more.