It is your own body, you should decide what to do with it. I know that people donating organs saves lives. I switched to being an organ donor last month. I'm dead, I don't need them.
But if you were to try and make this mandatory, would you also make people donate their blood while alive? It also saves tons of people. I have donated blood in the past a few times. Everytime that I was able, and not anemic, I would donate. My brother actually had to receive 12 pints of blood during one surgery. I am thankful for people that donate their blood and organs to help others, but it should be on a voluntary basis. I hope that one day my organs go to good use, and I keep living on in the body of someone else.