Do you have a right to die? The answer is not straightforward.

You can allow yourself to die.

In the 1990s the Supreme Court ruled that if you are a competent adult you have a constitutional right to refuse all medical treatment, even if that treatment is keeping you alive. Say you cannot breathe on your own, and physicians have attached you to a machine that breathes for you: you may insist that this machine be removed.
In other words, you may allow yourself to die, even when lifesaving medical treatment is available. You may even refuse food and water, if that is your preference.
Roughly, this ruling is based on (1) the principle of bodily autonomy, which says that you are in charge of what happens to your own body, and on (2) the principle of self-determination, which holds that, in matters that have little effect on others, competent adults should be free to decide how to live.

In most states, a physician cannot help you kill yourself.

But while you may allow yourself to die, according to the Supreme Court, states may still stop your physician from helping you to die, and most states do.
Only five states (Oregon, Montana, Vermont, California and Washington), as well as the District of Columbia, have legalized physician-assisted suicide.
In these states, patients who are terminally ill (likely to die within six months) and who are competent adults may, upon request, receive a prescription for a medication that they may take to kill themselves quickly and painlessly.
Of course, it is far from clear why any state may stop physicians who want to help patients kill themselves, even though all states are constitutionally forbidden to interfere when a physician helps patients allow themselves to die. In the one case, the patient dies after opting out of lifesaving treatment, while in the other a patient takes a prescription that ends her life. But both decisions are supported by the principles of bodily autonomy and self-determination.
There’s one more important layer of legal and moral complexity.

You cannot have a doctor kill you.

Even in the states where physician-assisted suicide is legal, “euthanasia” is not. Euthanasia means that the physician directly administers the medication that kills the patient, rather than merely giving the patient a medication with which they can kill themselves.
In no part of the United States may physicians directly kill their patients, even by request, even if it ends suffering that otherwise would be relentless, and even if those patients are terminally ill and physically unable to take their own lives.
If we have the right to decide how to live, don’t we have the right to decide to die, and to enlist the support of others who are willing to help?
It is not clear why states that do permit physician-assisted suicide nevertheless forbid euthanasia. If it is appropriate to legalize physician-assisted suicide in the case of competent, terminally ill adult patients who request such help, why wouldn’t it be appropriate to allow physicians to painlessly kill competent, terminally ill adult patients who request that sort of help?
In the one case, the patient does the killing; in the other, the physician does. But in cases where it is appropriate for a physician to help a patient to kill himself, why isn’t it also appropriate for the physician to kill the patient?
As far as I can tell, the answer is that both are appropriate, but opposition to both is widespread. I will close by sketching, and briefly rebutting, the case against both offered by the American Medical Association (AMA) in its opinion statements.

The AMA’s arguments fail.

According to the AMA, both physician-assisted suicide and euthanasia “would ultimately cause more harm than good,” both “would be difficult or impossible to control and would pose serious societal risks,” and both are “fundamentally incompatible with the physician’s role as healer.” The AMA adds that euthanasia as conducted by physicians “could readily be extended to incompetent patients and other vulnerable populations.” However, the AMA’s reasoning is unconvincing.
Far from causing more harm than good, well-designed policies of physician-assisted suicide and euthanasia would prevent patients from enduring great misery. Admittedly, the deaths of those patients would be terrible for the family members left behind, who are deprived of the benefits of a shared life. But the family members are in for great hardship either way — given that that their loved ones face prospects that are so grim that they wish to die.
What about the claim that physician-assisted suicide and euthanasia “would be difficult or impossible to control, and would pose serious societal risks”? It is not easy to guess what risks the AMA has in mind, but the worry appears to be that physicians who help patients die will end up killing people who have no wish to die, such as mentally deficient persons and the elderly.
If that is the concern, then the AMA must surely justify its position. As things stand, the evidence is against them, for in places where physician-assisted suicide or euthanasia have been permitted, the data present no grounds for concern.  For example, Oregon (where physician-assisted suicide is legal) reports no cases in which a request for lethal medication was coerced.
As for rejecting assisted suicide and euthanasia on the grounds that they are “fundamentally incompatible with the physician’s role as healer,” consider that the AMA does not oppose expanding the role of the physician to include such things as crime fighting (plenty of people use their medical expertise as consultants, as coroners and as forensic pathologists) or enhancing people’s appearance (e.g., by helping to develop beauty products, or performing elective cosmetic surgery).
Consider also that nothing stops physicians from healing some patients and helping other patients to die, just as veterinarians heal some people’s pets and euthanize others.
Let me sum up:  the principles of bodily autonomy and self-determination support our right to refuse treatment, thereby allowing ourselves to die.  Yet these principles also suggest that we may kill ourselves, and if that is so, surely we may enlist the help of others who are willing to help us end life, even if that means killing us.