Article IV, Section 1 of the U.S. Constitution states, in part: "Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State." This means that, the so-called "Defense of Marriage Act" (DOMA) notwithstanding (because it's clearly unconstitutional), New York and all other states are required to recognize marriages completed in any other state.

So if DOMA is unconstitutional, why hasn't it been struck down? Because it hasn't been challenged. In order to challenge a law, you must be directly affected by that law. In other words, a couple must get married in one state, then move to another state and be denied the full rights of marriage under DOMA. Then, and only then, can DOMA be challenged. Only recently have same-sex marriages begun to be performed in Massachusetts. There was a possible case (I'm not sure where it stands now) where a same-sex couple married in Massachusetts moved to Rhode Island and then filed for divorce. The last I heard, officials in Rhode Island hadn't decided whether to grant it, or deny it because of DOMA.

Governor Paterson is simply upholding the U.S. Constitution, as he pledged to do when he assumed the office of Governor.