How Much Is That Kidney In The Window?
For kidneys, since living people need only one to function,Virginia Postrel (a donor herself) suggests donor chains and financial incentives. From The Atlantic:

Such proposals, of course, attract vehement opposition from people who fear that financial incentives would squeeze out unpaid donors, entice the poor into bad medical choices, or "cheapen the gift." Some volunteers would undoubtedly drop out, relieved to let someone else provide their loved one's new kidney. But real incentives, rather than token rewards, would produce a net increase in the number of transplants. Giving a kidney to a relative or friend could still speed up the process, providing an incentive to do so but relieving such donors of any sense of emotional blackmail.

A well-designed system could address the concerns about donor welfare by including educational programs, waiting periods, and follow-up care for donors, and possibly by allocating the payments over time rather than offering immediate cash. As for "cheapening" donation, Matas notes the importance of attitude. "We need to create a culture of dignity. There are many people who want to do this, and the incentive would push them over the edge," he says. "The message should be, 'We can compensate you but never repay you.'"

Outlawing payments to donors is ostensibly a way to keep the system fair, giving rich and poor an equally lousy chance of getting a kidney. But wealthier people can already more easily register at distant centers with short lists. They're also more likely to have friends and relatives who can afford the nonmedical expenses that living donation often entails, including time off from work, child care, hotel rooms, or cross-country travel. (It is legal for recipients or third parties to pay such expenses, but, unlike medical costs, they are not covered by insurance.)

Patients with enough money and the right networks have yet another option. They can go abroad, to countries where the authorities sanction or ignore payments to living donors. That's how Henry David got his new kidney.

...Such "transplant tourism" is growing. Many of the transplants are not as medically sound as David's, and the care for living donors, even when adequate, rarely meets U.S. standards. Laparoscopic surgery is a First World luxury, as are desk jobs to which donors can safely return soon after surgery. With few protections beyond the surgeon's need to maintain a good reputation among potential donors, kidney vendors may not receive the full payments they're promised. In China (which is not where David went), organs may come not only from paid living vendors but also from executed prisoners. Transplant tourism is, in short, an ethical morass.

It is also a completely predictable byproduct of the current system, willed into being by policy makers who ignore the plight of kidney patients and by doctors who see above-board payments--and the protections of contract and malpractice law that would go with them--as pollution. Living donation is a low-risk procedure for the donor that offers life-changing rewards for the recipient. Yet the donor is the only person involved in the process who receives no compensation. "There's no reason that someone who does this should not get something substantial that will make a difference in their lives," says David. To people who like to celebrate living donors as heroes, payment seems terribly crass. But the vicarious thrill of someone else's altruism comes at a terrible cost.