This is a tough one, as there are many factors involved.
I believe that on other-than-conscious levels, everyone chooses the time and manner of their deaths. I also don't hold the belief that death and illness is necessarily bad, rather, natural expressions of a persons inner beliefs and realities (and therefore, self-created). If disease is self-created, then it should follow that diseases are self-healed too. Now, because most people do not agree, and most believe that disease and death are the result of external forces beyond their control (God, viruses, or radiation for example), that health must come from an external source too (priests, doctors, pills, surgery). So any treatment must come, in that case, from external sources. There is also the belief that to be sick or to die is a very bad thing, which results in, what I think, rather extreme measures to lengthen a life at any cost.
Now, given all of that information, I feel that for me personally, I would not choose euthanasia, but neither would I choose a stupidly lengthened life at the expense of quality of life, I would rather die of it, our figure out how to heal all by myself. However I do also think that it is an important option to have open to everyone, if they feel it necessary.