Each state regulates who can marry. Every state has an incest law, which prohibits to one degree or another, the marriage of individuals genetically related to each other. Obviously, parents are prohibited from marrying their children, uncles and aunts can't marry their nieces and nephews, and brothers and sisters are universally prohibited from marrying each other as well. These rules vary state to state. For example, some states may prohibit marriage between first cousins.
Some states prohibit adopted siblings who share no genetic link, from marrying.
The age at which marriage is permitted varies from state to state as well. Sometimes, an arbitrary age limitation can often be waived by a judge for good cause. Times are changing. In the past, all states required that the parties to the marriage to be one male and one female. Next, some communities began to recognize same sex marriages.