States where gay marriage is illegal include the majority of states in the US. Recent legislation has decreased the number of states where gay marriage is illegal to 35, and the LGBT community celebrates every time another state recognizes the constitutional right of gays and lesbians to marry. Believe it or not, there are still scores of things gay people can't do legally in the United States, but little by little gay marriage is being eradicated from that list.
US States that do not allow same sex marriage include notorious right leaning states like Texas and Kentucky as well as states that are not typically thought of as gay unfriendly like Illinois. Some states that don't recognize gay marriage honor same sex unions without the full privileges of marriage, but these are the states that do not allow full gay marriage rights.
What states do not allow gay marriage? Where are same sex unions illegal? Names of states where gay marriage is illegal are all here on this list of US states that do not allow same sex marriages. Hopefully there will be fewer state names on the illegal gay marriage list soon, but for now, these are the places to stay away from if you're looking for marriage equality (or head to if you believe in hetero marriage only).