I must admit that I'm a bit torn on this particular issue. I, myself, am not an organ donor. Why? Because I want to be prepared just in case there is some sort of afterlife in which my vital organs may be needed. Anyway, that's the short answer for why I choose to not be an organ donor, but it goes deeper... I still haven't decided whether I wish to be buried or cremated once I finally die. If there is an afterlife of sorts in which I would need my earthly form intact, I would take comfort in being buried with my body unaltered. Why should I have to donate my eyes to some blind bastard, lest I suffer in the afterlife without being able to see?! Also, on the same side of this coin, I am concerned that any part of my living flesh that may be put into another human being may still hold a portion of my consciousness, leaving me to experience the continued existence of the organ's recipient through his/her senses, unable to control any aspect of this new life for said organ.
Aside from theological aspects, here's what really divides me on this issue. As a modern Druid (or Secular Humanist), I fully support the advancement of the human species via science and technology. In this perspective, I should want my body donated to science once my life ends. However, I also feel that the earth is over-populated by humans as it is, and if my body is destroyed/buried in its entirety after my death, this may increase the chances of hindering the bearing of posterity by those who may benefit from my donated organs.
It is for these reasons that I (at this point in time) have chosen not to be an organ donor. To some, this may sound selfish, and it is to some extent. However, it's also about preservation of our planet and to keep our species from over-populating and dying off completely. If that makes me a selfish asshole, then so be it.
SIDE NOTE: This essay is far from being my complete view on this issue as it is more of a "reader's digest breakdown", feel free to contact me directly for further deliberation.