Here's an attempt to be controversial.
Here in the UK we have a chronic shortage of organs for transplant. There are several reasons for this, but the main one is what people simply don't seem to be too bothered. Carrying a donor card is not enough because your next of kin need to give consent as well (weird, I know). And while many people are happy for their organs to be used in principle, in practice they do not even carry the card or make clear to their next of kin what their wishes are.
Now, I expect we can all agree that organ donation is a good thing. But there is also a consensus that selling organs is bad form and I find myself wondering why this is. I am currently only considering organs from dead people rather than sad cases of someone who is alive selling a kidney. Also, ignore the scare stories about killing off slum children for their organs. There is no reason that NHS hospitals would use organs that did not have a crystal clear provenance. Setting up a market would not be very hard and policing it would be easy enough too. So, I think the abhorrence of selling organs is largely a matter of taste.
Here's a suggestion: when we take out life insurance, we could also sign a legal document that allows the insurance company to harvest our organs if they are useful. The company would sell the organs on to the NHS or private hospitals at whatever price the market at the time was demanding. In return, the donor pays lower life insurance premiums because the insurance company expects to be able to get something back from the organ sale. Furthermore, insurance companies are exactly the right companies to manage the risk of valuing a future asset. As the whole thing is voluntary, there are no ethical issues I can think of.
So a part from being in bad taste, what is stopping us from setting up a market in a desperately needed resource that would result in everyone benefiting? I'm really not sure.