Euthanasia and Buddhism
I've been to a lecture in which a Tibetan Buddhist monk (specifically, a nyingmapa) was asked the same question by a teenage girl. Basically, his answer was, such killing would both end some existing suffering and create some new suffering. Because regular person does not see all complexity of karma network spanning multiple lives, his or her acts are very likely to make the karmic situation even worse.

According to that monk, compassionate killing should be left to either dakas/dakinis (the crazy yogis capable of "eating icecream and shit at the same time" -- i.e. skilfully dealing with consequences of the bad karma they take on) or omniscient buddhas who can grant liberation at the time of killing, or at least create a favorable karmic condition in subsequent lives.