Every state, as far as I know, recognizes a right to self-defense as a matter of state law. Nowhere in the United States Constitution is there an enumerated right of self-defense. The Ninth Amendment to the United States Constitution -- long (and foolishly) disliked by certain conservatives because of its use to support a woman's right to have an abortion -- states, "The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people." Will a right of self-defense be the next unenumerated right recognized by the courts?
An interesting blog run by Law Professor Eugene Volokh discusses whether self-defense is now a constitutional right implied by the Heller v. District of Columbia decision that struck down DC's gun ban in part to permit self defense in the home.