All religions are unanimous in prohibiting active euthanasia as nobody has the right to take away life, even if that life is vegetative (eg, according to Jewish theology, a fraction of infinity remains infinity). There are controversies on passive euthanasia; all religions nevertheless agree not to confuse the maintenance of life and therapeutic relentlessness.
With regard to transplantation, most religions have in common that: (1) the transplant should be a gift from the donor, clear, free and anonymous; (2) respect for the wishes of the deceased; (3) certainty of the irreversible character of death; and (4) respect for the appearance of the corpse. In addition, they affirm that transplants should only be carried out with the therapeutic aim to save a human life and not to experiment. Agreement on these points applies to the following religiouns: Catholic, Orthodox, Protestant, Muslim, Buddhist and part of Judaism. On the other hand, Hinduism and Shintoism are against transplants; this is why there are virtually no liver transplants in Japan except from partial transplants from live donors.
One problem lies with the definition of death. For all the religions so far mentioned, the criterion of death is cerebral death. However, for Islam it is the definitive stopping of the heart, often making it impracticable to transplant from dead donors, although there is a progressive tendency (rejected by strict Islam) to accept cerebral death. But even if a donor has given consent whilst alive, it is the right of his heirs to dispose of his body after death and they can annul the consent. For strict Judaism, death is defined as the simultaneous abolition, total and irreversible, of the respiratory, cardiac and neurological functions, theoretically making transplants impossible. In practice, there is a favourable tendency to transplants developing due to two ideas: (1) the transplanted organ lives again; (2) the transplant aims at saving a life and it prevails on all the interdictions of the Torah.