Good questions, Nathaniel. I'll do my best to answer from my perspective.
Should suffering, terminally ill people have the right to end their own lives?
In my belief system (Christianity), life is God's gift, and only God can take it back again: so suicide is always sinful. In times past, suicides were denied burial in consecrated ground because of this, but nowadays, we accept that anyone who commits suicide is, by definition, not in his/her "right mind", and is under some awful compulsion, so this stricture is no longer applied. For those who hold to my belief system, therefore, I would say that suicide even in the case of terminal illness is not acceptable. However, I also hasten to add that I cannot and do not wish to impose my beliefs on those who don't share them - so for those from other (or no) belief systems, they must be guided by their own conscience.
That said, the Catholic Church's position is that if one is in serious pain, and terminally ill, one has the right to be pain-free. It is not sinful or wrong to prescribe large amounts of medication to control pain, even if this has the effect of shortening life - the intention is to decrease pain, not to kill. This is a fine moral distinction, but it's there, and I agree with it. It's the same with abortion: this is always and everywhere considered mortally sinful, but in a case where (for example) a woman who's two months pregnant is diagnosed with cancer of the cervix, and the operation to save her life will also kill the child within her, this is not considered abortion. The object, the intention, of the operation is to remove the cancer. A side-effect of the operation is the death of the child. The harm to innocent life is regretted, and is not the primary intention or purpose of the surgery: therefore, the termination of the pregnancy is not considered to be abortion as such, and is not considered wrong or sinful.
This is known in moral theology as the theory or principle of "double effect". An action may have two (or more) results or consequences. As long as the primary intention, or effect, is morally and/or ethically good and acceptable, the secondary effect associated with the primary effect, even though bad in itself, is allowed. However, if the primary effect is evil, the secondary effect is never acceptable, even though it may be good.
If they want to do so and are not capable of doing it themselves, should they have the right to get help?
Here I have to say no, in the context of Christian belief. If it's wrong for you to kill yourself, how much more so to implicate another in your wrongdoing! Of course, if you don't believe that what you are doing is wrong - in other words, if you're operating out of another belief system, not Christianity - then you'll have to make up your own mind on this.
However, it's not wrong to seek help for pain relief, even if this means a life-shortening effect in terminally ill patients, and Catholic doctors, nurses and hospitals are explicitly permitted to offer such pain relief - see my explanation above.
This does create problems where (for example) a patient may want to end his/her life, and appeals to others for help, but they can't morally do so on the basis of their own beliefs. It also creates legal problems under laws such as those pertaining in the USA, where many patients in great pain complain that their doctors won't prescribe adequate strengths and/or quantities of pain-killing narcotics, for fear of running foul of the DEA and the War On Drugs. Special legal exemptions have had to be made for medical personnel in hospices, for example, where the use of pain-killers is much higher than in normal hospitals, otherwise they would not be able to function.
If so, who should help?
This is a problem for the patient to work out with those who share his/her belief. I absolutely reject any attempt to make it a legally binding duty on medical personnel to assist the patient to die. Quite apart from the moral issues raised, this also brings up the point I made in my earlier post, that sooner or later, those medical personnel are going to be making the decision themselves - if not for their own convenience, then for the benefit of the hospital employing them.
Another legal problem here is the relationship between the patient and his/her family on the one hand, and the medical establishment on the other. Let's say the patient is in great pain, and asks the doctor to help him/her to die. The doctor agrees, and provides the drugs, or prepares and administers a lethal injection, or something like that. Later, it emerges that the patient belonged to a very religious family, who are unanimous in their assertion that the patient would never, ever have asked for something like that, and any attempt to say that he/she did so can only mean that this was coerced by the hospital and/or the doctor. They sue. Who wins? Basically, that doctor and/or hospital are in a no-win situation... even if they are found innocent in court, they'll be smeared forever as "Doctor Death" or "The Hospital Of Death". Only when all parties are able to consult and agree on this can there be any suggestion of willing assistance by medical staff - and, as I said earlier, this is open to enormous abuse, which is very likely to occur.
Fundamentally, one cannot ask another person to do that which is morally evil or repugnant to that person. You may be my best friend, but if you ask me to help you to die, the answer will be "No". I shall certainly help you in any way that I can, even to the use of pain-killers in quantities that may shorten your life: but you can't ask me to ignore my own conscience.
