I find it odd that people have serious reservations about euthanasia still. This isn't to say that there aren't serious considerations that need to be taken into consideration about whether it should be performed in this instance or that instance. But the act, generally, is hard to deny.
Perhaps, its because of its association with the Nazi party that really made things difficult for euthanasia to gain a foothold in the public consciousness. I think, though, this is a product of the unfortunately powerful Nazi propaganda machine more than anything. To say that the Nazi's engaged in euthanasia is like saying a straight man is being discriminatory towards males. Its a misuse of the term.
When the Nazi's utilized "euthanasia" the state determined when it was acceptable for a person to live or die, not based on any particular medical condition, patient desire, or quality of life issue, but rather based on a perceived inferiority of a particular group. We properly call this genocide, and although many today call it that, its hard to shake the synonymous relationship that history made between genocidal acts and euthanasia.
When I speak about euthanasia, I'm referring to a medical practice of terminating a life because the person is terminally ill. The least controversial form of euthanasia, is voluntary euthanasia, where the person to be euthanize is terminally ill and requests euthanasia. There are cases that fall in-between these definitions, and although they are very difficult, I wouldn't call them euthanasia. I'm thinking of cases in which a person is not terminally ill, but requests to be killed because of quality of life issues and their inability to terminate their own lives. The film "Million Dollar Baby" is a good example of such a case.
Surely, we can see the moral differences between the Nazi genocide program, and euthanasia. The Nazis murdered people who wanted to continue to live. If they did want to die, it is most likely because of the conditions that the Nazi's forced them to endure within concentration camps. Causing a person to suffer from a terminal illness is just as bad as murdering them. In the case of euthanasia, assumedly, the doctor or the government did not cause directly their current afflictions, nor is their choice for living out the remainder of their life taken away from them.
Old associations die hard though. (This is by no means a full account of why euthanasia is acceptable. This is simply an account of why a very common objection to euthanasia is not a powerful objection.)