I think there are several issues that previous posters have alluded to:
1) assisted suicide by coherent adults -whether by living will, do not resusitate order, etc. absolutely! I personally think that the two adult deaf men who 'killed themselves' were not right in their decision. (I put 'killed themselves' as it's actually a Christain concept, in the acient world, killing oneself by receving a 'sign from 'god' and or being faced with physical or mental anguish was considered completely acceptable, thereby the Roman idea of leaving the disgraced man alone with a dagger, etc, whereas in Christainity, it becomes a rejection of 'god')
2) TBH, I cannot agree with euthanasia in any form. If the person understands, then it becomes 'assisted sucide', but otherwise, it is not and in my opinion, if the person involved cannot assist in the decision making, then no. This is a tricky one, because a 1 year doesn't have the cognitive ability to argue their case for life or death, but for children, I just couldn't. What if there was extreme suffering or a vegative state and then, we come into an even more grey area - what is rational thought and what is existence? thereby, leading to no. 3
3. Vegative state or aware? If in a vegative state, please let me go. My OH disagrees - he wants to stay in his physical form as long as possible in the hopes of finding a cure of what sent him into that vegative state. However, in that instance -- of a vegative state, then perhaps euthanasia is acceptable as the person (with at least 2 or 3 medical personnel agreeing, NOT the family), isn't actually a 'person' anymore -- that the soul (if you believe in that) has already escaped.
I hope I haven't offended anybody, but I do think it is a case-by-case situation and in mine, let me go -- but make it MY decision!
best wishes