Not every Jew is a reliable source of general information about Judaism. Not all of us have had extensive Torah education, for starters. Some Jews will say, “I don’t know, ask a rabbi” and others will tell you what their bubbe [grandma] told them on the subject. For them, that might be more authoritative than any rabbi.
One of the subjects where there are a lot of bubbe-meisers [grandma stories] going around is organ donation. The fable you might hear is, “NO! If you allow someone to harvest organs from a body, it can’t be buried in a Jewish cemetery!”
The question of organ donation is complex. If we are talking about a donation from a brain dead body, and it will almost certainly save the life of the recipient, then Reform, Conservative, and many Orthodox sources agree, this is not only a permitted donation, it is a mitzvah. The principle involved is pikuakh nefesh – saving a life.
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. – from Synopsis of Teshuvah on Organ Donation, by Rabbi Joseph H. Prouser (Conservative Movement)
However, that’s the big picture. What about the donation of corneas, which give vision to the blind but do not technically save a life? What about donations that will extend medical knowledge, but not immediately save a life? In such cases, I’m going to say this: talk to your rabbi. Not some random rabbi, not some rabbi on the Internet, but YOUR rabbi. Don’t have a rabbi? If you are serious enough about being Jewish to have such questions, then you are serious enough to need your own rabbi. Get one.
Know that the Internet is full of “authorities” who make all sorts of pronouncements. You can likely find someone who says anything you want to hear, whether that’s “anything is OK, don’t worry” to “no organ donations from a dead body ever, under any circumstances.” The Internet is the Wild West: anyone can call themselves “rabbi” but that doesn’t make them one, nor does it necessarily make them the right rabbi for you.
Questions like the ones above require conversations. You may say, “It’s a simple yes or no!” but no, it isn’t. A lot depends on how you understand Jewish law or tradition (and as much as some folks would like you to think there’s one proper way, no there is not – not even among Orthodox communities and rabbis) and a lot depends on the fine details of a situation. So you need to talk to a rabbi.
And now I hear it coming in the Comments: What do you think about the fine points, Rabbi Adar? What’s on your organ donation card? And here, because I so badly want you to get your own real live actual rabbi, I’m going to say, “None of your business.”
Bottom line: Judaism does not have a blanket condemnation of organ donations. In some situations, organ donation is a big mitzvah. For more than that, talk to your rabbi.