The inestimable value of human life is a cardinal principle of Jewish Law. This value is expressed through the religious obligation for self-preservation, as well as the duty to save the life of one's fellow human being, if he or she is in mortal danger. This religious obligation is a mitzvah of such a high order that it takes precedence over virtually all other religious duties with which it may conflict: the sick must eat on Yom Kippur; the injured are treated on the Sabbath; we postpone the circumcision of weakened infants beyond the covenantally mandated eighth day, etc.
Since the onset of the modern era of organ transplantation in the 1950s, leading rabbinic authorities from throughout the religious spectrum have seen in this new technology a new and effective means of fulfilling a divine mandate to save life – an obligation first expressed in the Torah itself: "You shall not stand idly by the blood of your neighbor." Organ donation is a new means to fulfill an ancient, eternal religious duty: a mitzvah of the highest order.
The Committee on Jewish Law and Standards has affirmed this principle in unambiguous terms, and celebrates the leadership and insight of other movements and authorities who have shared the task of educating the Jewish community about this mitzvah: "The preservation of human life is obligatory, not optional. Since all conflicting halakhic duties are suspended and human lives are at stake... consent must be granted for post-mortem organ donation when requested by auto insurance doctors and hospitals for use in life-saving transplantation procedures.... This applies to the individual in anticipation of his or her own death, as well as to health care proxies or next of kin whenever they are legally empowered to make such decisions on behalf of the deceased.... By so doing, he or she renders only profound and genuine honor to the deceased."
– Synopsis of Teshuvah on Organ Donation, by Rabbi Joseph H. Prouser
More information and an organ donor card can be found here.