I believe strongly in liberty and personal freedom. Under ideal circumstances, I feel it would be perfectly acceptible to sell a kidney.
Unfortunately however, I think in our current monetary environment (i.e. fiat currency with bankers controlling the world) allowing the sale of kidneys is to invite trouble.
A poster gave the example of a man who was auctioning his kidney in order to pay off some debts.
If we legalize the selling of organs, and the sellers' primary motivation is to escape burdensome artificial debts caused by a morally bankrupt system of currency and fractional reserve banking, then we invite further exploitation of the people.
I vote NO to kidney selling as long as we have fiat money and a country run by special interests.
misterbig makes a valid point here - the order in which libertarian principles should be implemented is crucial. Other, more fundamental infringements of our liberty may need to be be fixed before we can allow for this. To give an example, consider this horrifying scenario: We decide that, as our first step toward restoring the republic, we are going to make it legal for anybody to sell their organs for money. By extension, we make the grave mistake of classifying a person's organs (along with the rest of the body) as mere possessions owned by the person, ignorant of unforeseen implications. Since our entire monetary system revolves around debt, a LOT of people are indebted to others. Now...consider what would happen if someone went bankrupt. In such a situation, people are generally forced to surrender most of their marketable assets to their creditors...now, if we consider your organs to be marketable assets, can they be seized by your creditors?

I imagine people like us would be smart enough to foresee such a situation and write in a "caveat" in the law legalizing the sale of organs to prevent such abuse, but...despite the hyperbolic aspects of my example, I hope it helps illustrate the general point that we'd be wise to prioritize certain libertarian policies before others.
As another example, the big-L Libertarian Party advocates completely open borders - while I disagree with this even in principle, my disagreement is outside of the scope of this example. What
is important is that under a laissez-faire free market with steady growth, Libertarians note that we would no longer be subsidizing freeloading and the economy could soak up unskilled labor like a sponge (i.e. wages would not depreciate, because the supply of jobs would grow along with the demand - I agree with this principle in general, but I imagine it would take a generation or so of free market policies for a large middle class to reemerge in earnest - and until then, unrestricted immigration is kind of out of the question

). However, even assuming this is true, it would be absolutely disastrous if we tried implementing such a policy
before getting rid of the subsidies and government intervention in the economy!