The final answer to this question will be one of personal liberty and conscience in Christ. The Swiss Second Helvetic Confession deals at length with the burial of the dead in chapter 26, paragraph 1. This section answers most of the questions about what we should do with the body, and indirectly this question concerning organ donations.

The Burial of Bodies. As the bodies of the faithful are the temples of the Holy Spirit which we truly believe will rise again at the Last Day, Scriptures command that they be honorably and without superstition committed to the earth, and also that honorable mention be made of those saints who have fallen asleep in the Lord, and that all duties of familial piety be shown to those left behind, their widows and orphans. We do not teach that any other care be taken for the dead. Therefore, we greatly disapprove of the Cynics, who neglected the bodies of the dead or most carelessly and disdainfully cast them into the earth, never saying a good word about the deceased, or caring a bit about those whom they left behind them.

Two Scripture passages tell us more:           

And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.

Revelation 20:13

And though after my skin worms destroy this body, yet in my flesh shall I see God: Whom I shall see for myself and mine eyes shall behold, and not another; though my reins be consumed within me.

Job 19:26-27

Why do the sacred Scriptures mention that the sea will give up the dead? Why not speak about those who were burned up or otherwise left no mortal remains to be buried? For practical reasons those who go to the seas have buried their dead at sea. There is no preparation of the body and for the most part the inhabitants of the sea will consume the body. This is a very visual reference to the resurrection of those who left behind no physical body to resurrect. No part of this body is needed for the resurrection in the last day. The resurrected body has no need for any of its present parts which will not still exist in their present state no matter what form of burial is used as noted above in the passage from Job.

"Can parts of the body be removed for use in bringing sight or life to another without desecration of the body of the deceased?" is the only question that appears to matter to the Christian. The answer is yes and without it causing disfigurements that happen naturally in almost all accidental deaths. There is no direct mention in the Bible of organ donation. However there is also no reference whatsoever that would preclude donation of organs before or after death. The choice then is one of conscience and neither right nor wrong from a biblical perspective.