First, we must define a few terms. Euthanasia might be described as mercy-killing, the act of killing someone who is suffering badly, without the consent of that person. There is no state in which this is legal, nor is there any federal law that makes this act legal. It is considered a form of homicide in every American jurisdiction. Physician-assisted suicide, on the other hand, is suicide with the help of a doctor, so the person is making the choice to die, as contrasted with euthanasia, for which the person dying has made no choice at all.
There are only four states in which physician-assisted suicide is legal: Montana, Oregon, Vermont, and Washington, through common law, referendum, or legislation. The majority of states, 42, have legislation prohibiting physician-assisted suicide, or it is prohibited as a matter of common law. The remaining states are "silent" on the issue, having no laws for or against.
At the present time, there is no federal legislation on physician-assisted suicide at all. This can be framed as a constitutional issue, under our rights to privacy, and this has been upheld for the state laws that allow it, but thus far, there has been a willingness to allow each state to make its own choice on the issue, and to the best of my knowledge, no Supreme Court opinion that makes this "the law of the land."