There are only 2 states at this point you can get married in- California and Massachusetts. For both states, the age requirement is in general the same - 18 for both parties. Of course, since it is "marriage" there are permissive variances that may allow someone younger that that to marry. These would require parental permission, or a bypass by the court.
18 is the legal age in California & Massachusetts, although a judicial bypass should be available. Connecticut has just allowed marriage, and New York State recognizes marriages in principal.