Here's the opinion of His Holiness the Dalai Lama, someone who is much more relevant on a Mahayana
Buddhism forum than say, the Pope:
"Dalai Lama backs euthanasia in exceptional circumstances
Asked his view on euthanasia, the Dalai Lama said Buddhists believed every life was precious and none more so than human life, adding: "I think it's better to avoid it."
"But at the same time I think with abortion, (which) Buddhism considers an act of killing ... the Buddhist way is to judge the right and wrong or the pros and cons."
He cited the case of a person in a coma with no possibility of recovery or a woman whose pregnancy threatened her life or that of the child or both where the harm caused by not taking action might be greater.
"These are, I think from the Buddhist viewpoint, exceptional cases," he said. So it's best to be judged on a case by case basis."
From http://www.tibet.ca/en/library/wtn/arch ... m=9&p=18_4
Also, from the early 90's, HHDL again on the same topic - including abortions:
The Dalai Lama, the 1989 Nobel Peace Prize winner and the self-exiled leader of Tibetan Buddhism, says that abortion and euthanasia are permissible under certain circumstances but that neither should be widely performed.
While on a national tour that brings him to UCLA today and UC Santa Barbara on Sunday, the Buddhist monk told a Houston audience this week that, "generally, abortion is not good" but that it "may be justified" in cases where the child would be born badly deformed or "the mother will suffer."
Speaking at Rice University, he said birth control should be used to prevent unwanted pregnancies. The best form of birth control is to become "a monk or a nun," he joked. "If that is not possible, then other methods are quite OK."
He said that euthanasia, or mercy killing, is a "very complicated" issue but that "from the Buddhist viewpoint generally speaking it is not good." It should only be performed, he said, where it is considered best for the "larger society," or for the patient himself.
From http://articles.latimes.com/1991-04-06/ ... dalai-lama
Also, Ringu Tulku Rinpoche speaking about euthanasia: