Many U.S. states have had their bans on same-sex marriage struck down as unconstitutional because they violate the "Equal Protection Clause" of the US Constitution, contained in the 14th Amendment.
The United States constitution does not discuss marriage. Essentially, this leaves control of civil marriage to the individual states.
If by "illegal" you mean "against the law," then none. There is no state in the US where same-sex marriage is considered a crime. In fact, in most US states, same-sex marriage is legally recognized. (See related questions below: "What US states have legalized same-sex marriage" and "What US states have banned same-sex marriage.")
Marriage law is within the jurisdiction of the States and, therefore, such an action would be a State matter.
It is a physical challenged on our government; but when we talk on States we should put the blames on the governors
If by "illegal" you mean "against the law," then no. There is no state in the US where same-sex marriage is considered a crime. However, in some US states, same-sex marriage is not legally recognized. (See related questions below: "What US states have legalized same-sex marriage" and "What US states have banned same-sex marriage.")
Japan
There are currently no laws prohibiting the marriage between two people of different races in the United States.
In September 2004, Mr. Kind voted against a constitutional amendment that would have banned same-sex marriage in the United States.
In September 2004, Mr. Hinojosa voted against a constitutional amendment that would have banned same-sex marriage in the United States.
In July 2006, Mr. Costa voted against a constitutional amendment that would have banned same-sex marriage in the United States.
In most states if there is no license, there is no marriage. Some states allow a common law marriage when people have been living together for many years.
Daniel Webster