I believe that donors serve a very important function. My uncle died waiting for a liver, so I may be a bit biased. (Quite a bit, actually.) However, only you can decide what is right for you. I believe that God would want us to help out our fellow man in any way we can, and I don't believe that He would have a problem with us donating blood, plasma, bone marrow, or organs. Especially when our life is over, wouldn't He want us to make the best use possible of the gift of life which He gave us in the first place?
Obviously, the Bible does not specifically address this issue, since the technology was not known or even dreamed of in those days. The mandate to "love your neighbor" was stated by Jesus (Matthew 5:43), Paul (Romans 13:9), and James (James 2:8), but it can actually be traced all the way back to Leviticus 19:18.
Are you talking about being an organ donor if you should die? If so, be guided by your own heart and conscience. Many religions discourage organ donation, but personally, I can't imagine anything more spiritually appropriate than giving the gift of life to another person. The only one who can make this decision for you is you.