From a Christian and/or Muslim point of view, is it a sin, or a good deed to save someone's life by donating your vital organs?

In Christianity, intentional sacrifice is a sin - it brings us back to the ancient times of idolatry where people would sacrifice others to please the gods. Your example is similar to suicide. Christians can't decide on their own when it is a good time to die. There are instances of course when one goes into extremes to protect others, but the assumption there is that there still is a small chance of surviving.

Just answering your "bold text question", the essence of all religions, be it Christianity, Islam, Hinduism, Jainism, Buddhism,...... is "Help Mankind", so whenever appropriate time comes, one should not retreat back, rather take courage and offer a helping hand. Remember "Saving someone's life"  is the greatest act of kindness a mortal can do.  So there is no point of Sin in this kind-full act.

You got us! No, seriously though. I see tons of questions like these, asked from the assumptions that 1. Christian ethics = utilitarianism, and 2. Christians are allowed to act towards others in safe knowledge that all we believe is true (e.g. why not kill him, he's going to heaven!) These assumptions are both wrong. They're also very obviously wrong, to anyone who's spent any serious effort at all understanding Christianity. My life is not only my own. I can't give anyone permission to do something that would kill me. No matter how good the outcomes may be, permission is not mine to give. (For that matter, you don't need to believe in God to think like that). I may risk my life. I may even do something that will tempt people to kill me. Jesus did, after all. But never give them permission beforehand. Forgiveness afterwards is usually an option, but you can never assume you will get it, that disproves its sincerity. (There's also the detail that you can't ask forgiveness of a corpse!). My obligation to respect life, including my own (love others like yourself, remember?) comes before any obligation to seek good outcomes.

I believe it is OK to recycle to better our quality of life and our environment.  I don't believe it's a sin to donate organs. If you are dead you won't need them and they will simply rot. God doesn't need your organs in heaven. Why would it be a bad thing to Dave someone's mother or child with organs you and God have no use for? God says to honor the mother and father. God says to love your neighbor. How much more honor or love can you offer a person, by giving them a new life or a better quality of life

I am a Christian and the Bible only tells us to abstain from blood. Organ donation is a personal choice but I found that many religious people don't understand organ donation. In order for your organs to be donated Doctors will have to keep your circulation going with the help of machines..but you are technically dead. So it is NOT suicide if you donate your organs. I personally dont want my life to be artificially extended for an uncertain amount of time but I like the idea of helping someone by donating my organs. I realise this is a conflict of interests but you can specify in advanced medical directive that you only want to be kept 'alive' until your organs have been donated. If you do so, its a nice thing you have done but whats more important is that you have been a good person during your lifetime who followed bible principles and helped people wherever they could.