You must meet certain requirements in order to marry. These vary slightly from state to state, but generally include:
being at least the age of consent (usually 18, though sometimes you may marry younger with your parents' consent)
not being too closely related to your intended spouse
having sufficient mental capacity -- that is, you must understand what you are doing and what consequences your actions may have
being sober at the time of the marriage
not being married to anyone else
getting a blood test (in just a few states), and
obtaining a marriage license.
Same-sex couples can marry in California, Connecticut, Delaware, District of Columbia, Iowa, Maine, Maryland, Massachusetts, Minnesota, New Hampshire, New York, Rhode Island Vermont, and Washington. All other states prohibit people of the same sex from marrying, though a number of states allow domestic partnership or civil union registration through which same-sex couples can obtain the rights and obligations of marriage. See Same-Same Marriage: Developments in the Law for complete information on same-sex relationship recognition.
All states prohibit a person from marrying a sibling, half-sibling, parent, grandparent, great-grandparent, child, grandchild, great-grandchild, aunt, uncle, niece, or nephew. Some states have additional prohibitions.