New York does not differentiate the validity of a marriage based on whether the parties to the marriage are of the same sex or different sex. The rights, benefits, protections, and responsibilities of spouses are the same. Since New York enacted the Marriage Equality Act in June of 2011, same-sex couples are entitled to the same process for marriage as opposite sex couples. Even if you are a same-sex couple that does not reside in the state, New York allows you to get married there.
New York recognizes civil unions that are created out of state. A civil union is a legal union between two individuals of the same sex. If you entered into a civil union out of state and are seeking to end it, New York can validly dissolve it for you. If you were previously in a civil union, but now seeking to get married in New York, you may want to consult an attorney about properly ending your civil union first as it may affect your marriage.
The state of New York does not recognize “common law marriage.” Common law marriage refers to a type of marriage that is not created through the laws on marriage, but rather by the conduct of the parties. Conduct such as cohabiting and acknowledging each other has husband and wife. To have a valid marriage in New York, you need to marry formally under the requirements of law, without that, parties cannot generally attain the rights that a married couple does at the time of divorce. New York may recognize a common law marriage if a couple now resides in New York, but previously followed the requirements for a common law marriage in another state. In that situation, you may have the same rights as a married couple does at divorce.