CWY links to a NY Times editorial that proclaims the death penalty unconstitutional. They offer no support for that proposition, only that "the Eighth Amendment bars capital punishment completely."
The most common argument I've heard is that the interpretation of what is cruel and unusual changes with time and therefore civilized society today considers the death penalty to be cruel and unusual. In other words, the moral and constitutional issues are intertwined and the death penalty is cruel and usual because it is morally wrong, and therefore it is constitutionally prohibited vis-a-vis the 8th Amendment.
CWY argues that the Constitution explicitly recognizes the death penalty in the 5th and 14th Amendment when it makes allowances for the taking of life with due process. If the Constitution implicitly allows the taking of life, how could it be cruel and unusual?
But let's assume the meaning of cruel and unusual does not hinge on how the framers understood the term. Certainly their society did not recognize the death penalty (as a concept) to be cruel and unusual. But if we construe the clause according to modern understanding, it would be cruel and unusual. Hence the 8th Amendment should bar capital punishment.
This argument fails though. First, even if we assume that the 8th Amendment changes with time, who said the death penalty is cruel? If the law allows the death penalty, we have to assume that a substantial percentage of the population supports its implementation. Unless the people wish to see a cruel practice continue, we must conclude they do not view it as cruel. So because a few judges, or academia, consider it cruel, their moral positions are dispositive? On what basis?
In order to prove capital punishment falls under the 8th Amendment's prohibition, opponents must show a large percentage of the US considers the death penalty cruel, and as long as the death penalty is on the books that will be impossible. So it's a catch-22.
Of course they might argue that world opinion considers it cruel and we should construe the clause based on how the world views it. Even if we accept the premise that foreign viewpoints are relevant to constitutional interpretations, the argument is false. What they mean is that Europe considers it immoral. But much of the world (Africa, Asia, South America) practice the death penalty. Obviously we do not have anything close to approaching a consensus, and so opponents have to show why Europe's position should be granted more weight than Africa's on this question.
But even if we assume that the 8th Amendment, properly construed, proscribes the death penalty, the 5th and 14th Amendments still sanction its use. When we have a general rule and a specific rule, a statutory rule of construction requires us to afford the specific rule greater weight. Here the 5th and 14th Amendment by implication openly support the death penalty while the 8th Amendment prohibits it as being part of a general class of cruel punishments. The 14th Amendment therefore should be read to create an exception to the class of punishments prohibited by the 8th Amendment (although the 8th Amendment could still prohibit certain methods of capital punishment). So no matter how one interprets the "cruel and unusual clause" the death penalty still is not unconstitutional.
Update: After reading my argument a friend made a good point. The 5th and 14th Amendments do not expressly allow capital punishment. They say no one shall "be deprived of life, liberty, or property, without due process of law." That merely implies that if someone was deprived of life, there must have been due process but does not expressly sanction capital punishment. It is procedural and merely requires due process if the death penalty is allowed. It basically means, "If the death penalty is allowed and it is going to be applied, then there must be due process." In other words, if the 8th Amendment forbids it, then this clause no longer operative because the death penalty cannot be carried out.
Interestingly, the 5th Amendment is written in the negative: "no state shall...." All the clauses are that way. Perhaps that's why the Due Process Clause is also in the negative, and the clause should therefore be read in its positive form.
Either way this argument only makes sense if one completely ignores the intent of the framers and original understanding of the clause. Clearly the framers intended to allow the death penalty since capital punishment was legal at the time. But the people making the argument are not Originalists, so those issues are either irrelevant or outweighed by other considerations.