People of the opposite who are living together can also form a legal relationship in the United States -- it's called a common law marriage. In the states that recognize those, the requirements are typically that couple lives together for a certain amount of time and hold themselves out to be man and wife.
What is interesting is that common law marriages are only recognized in nine states, but they can impact all states. For example, let's say a couple has entered into a common law marriage in Texas. That couple moves to Arkansas, which does not recognize common law marriages. Due to the Full Faith and Credit clause of the United States Constitution, an Arkansas court will have to view that relationship as a valid marriage if one of the "spouses" files for divorce, if one dies and a will must be probated, etc.
Here's a question that seems to be dangling -- if a couple enters into a same sex marriage in a state that recognizes those, what happens if they move to a state where same sex marriage has not be legalized and half of the couple files for divorce?