Jewish bioethicists, across the denominational spectrum, tend to consider that cessation of breathing (which is connected to brain stem activity) as the Jewish legal definition of death.
According to Orthodox rabbi and doctor Abraham Steinberg:
The talmudic and postâ€‘talmudic sources do not require the cessation of the heartbeat for the determination of the moment of death…when it is clear that independent breathing can never return because of the irreversible death of the brainstem, the patient can be regarded as dead from the moment that brainstem death is established, even if the patientâ€™s heart is still beating. (MORE)
But apparently there is still resistance to this definition of death from the Ultra-Orthodox community:
During a rabbinical conference held at a Dead Sea hotel MK Rabbi Moshe Gafni delivered a speech in which addressed the bill regarding brain-dead patients on respirators proposed by Otniel Schneller (Kadima), who was in attendance.
Rabbi Gafni objected to the position espoused by Schneller, who claimed that all gedolei Torah support the proposal. Rabbi Gafni said that in fact the opposite is true. Maran HaRav Eliashiv shlita issued instructions to oppose the law, saying that according to halochoh as long as the heart continues to beat the patient is considered alive in every respect and it is strictly forbidden to deny medical treatment, and as such UTJ has decided to oppose the bill. (MORE)