Ronald Reagan said that government is not the solution, rather it is part of the problem. People, however, can not always be trusted to do the right thing. Murder, of course, is forbidden--regardless of written or unwritten laws. I'm not sure I would ever be able to do it, but if a loved one of mine was in terrible pain from a terminal illness, I would want that person to be able to decide when it was time to go.
What would the practice of euthanasia look like if the government were not involved in regulating it? A truly liberatarian philosophy suggests government should not be involved in personal decisions like this, but the potential for abuse where euthanasia (as opposed to living wills) is concerned is staggering. The widespread abuse of any freedom or privilege is, to me, the very reason for government in the first place--to bring order to disorder. To protect the individual from more powerful mechanisms which threaten him.
Inevitably, the government--be it federal, state or possibly even local--will control this complex issue. More liberal-minded areas are more likely to allow it and probably have a broader base of support. Such states would undoubtedly try to overthrow any federal laws anyway. I think it really should be a personal choice, but most governments don't take personal freedoms into account when death is involved.
Euthanasia is obviously an extremely complicated issue, and so much depends on interpretation and what is meant by euthanasia, as pointed towards by #1. Given that we are referring then to assisted suicide, it depends a lot on how we define "liberty" and the necessary limits that the government chooses to place on this extremely complicated word.
I am not sure that the 9th Amendment is applicable to this issue; and the 14th guarantees one the right to life, liberty or property without due process of law. I am not sure that the right to die is constitutionally protected by either. A more appropriate argument might be the right to privacy which has been implied by the Supreme Court in Griswold vs. Connecticut. The right to privacy was also the primary issue in Roe vs. Wade, in which the court held that a woman has the right to her own body as her private property, and may choose to abort a pregnancy if she wishes during the first trimester. I would think that privacy is a much stronger argument that Euthanasia is constitutionally protected, provided it is consensual and the decision to end ones life is made with full knowledge of the consequences.
You could apply the 14th amendment "due process" and allow states to establish procedural hearings for those cases in which terminally ill people could request permission to end their own lives in accordance with preapproved standards. I suppose it could be similar to a probate proceeding or other proceedings such as those held for minors in order to avoid parental consent for an abortion.
I would want someone to allow me to die if I was in terrible pain. I think that this is a decision that a terminal person should be allowed to make for themselves.