As a premature baby is incapable of making descisions, the control of its existance falls to those who can. In this case primarily the parents, followed by the doctor, and then society (government) and such legislation that might pertain to the situation. I honestly have no right to become involved in such a personal choice as this, nor do I wish to interfere with what must be an already difficult situation. This falls into the realm of Abortion debate, and I hold the same opinion in that case.
The elderly, infirm, or dying Adult however should have the right to end a painful existance should they choose to do so. Attempting to decide for them is the worst form of arrogance, and in my mind rather disgusting.