In the long-awaited and much-discussed Nancy Cruzan case, a 5-4 Supreme Court majority ruled that absent "clear and convincing evidence" that a once but no longer competent patient wishes to discontinue her life support (in this instance artificial nutrition and hydration) a state is not constitutionally compelled to terminate that support.
Nancy's situation is tragic. Since suffering severe injuries in 1983, she has been in a persistent vegetative state. Yet medical experts testified that if her feeding tube were not removed she could linger on in her present condition for many years.
But the first thing to keep in mind about the Cruzan decision is that the question presented was not whether pulling the feeding tube under the circumstances is desirable or sensible, but whether it is constitutionally mandated. The Cruzan case went all the way to the U.S. Supreme Court because Missouri, the state where the litigation arose, applies a heightened standard of proof of a patient's wishes before life support could be terminated. The Court did not "approve" or "endorse" the Missouri standard; it simply found nothing in the Constitution that prevents a state from utilizing such a standard.
Kamisar, Yale. "The Right to Die: Green Lights and Yellow Lights." World & I (1990): 596-8.