I usually stay out of this debate, since the different sides are mostly irreconcilable due to the fact that the standpoints are ultimately grounded in emotion. Personally, I agree with Jay and Smeg. From any other viewpoint than that of a lust for revenge, the death penalty is unacceptable. Now, maybe some people on the anti-death penalty side do belittle the "lust for revenge"-aspect: if someone killed my children, for example, I might very well view it very differently. But the bottom line is that that view would be based on emotions like blind rage and a lust for revenge, and those are usually not good grounds to build a healthy society on.
The arguments that convince me of the death penalty's unacceptability are these: first, it doesn't work as a deterrent. That has been proven over and over again in practically every country and era. Criminals, especially murderers, often commit their crimes out of passion and lust with little beforehand reasoning of the consequences. Many times, they're so fucked up they don't even care what happens to themselves. The death penalty has been around since the dawn of civilization, and has it deterred crime? Hardly. The looming threat of execution has the effect of being the hardened criminal's last step of alienation from society, they argue that they've been receiving the short end of the stick their entire lives, and if the state is going to execute them anyway when they get caught, they might as well go on a killing spree or something. It is not a deterrent, it is a stimulant, fueling the merry-go-round cycle of violence in society as a whole. A testament to this is that countries that exercise the death penalty are usually more violent (both internally in having high crime rates, and externally as in fighting wars, etc.) than countries that have abolished it (there are of course exceptions, Japan comes to mind). So, I think that the anecdotal joke about the sheriff and the condemned man Jodo presented is a shadow argument, since the "deterrent effect" isn't about deterring the person in question, but deterring others from committing the same crime in the future (and here the death penalty has clearly proved it's uselessness throughout history). There is also in principle no argument in favour of having the death penalty instead of life imprisonment. Why not just lock them up for good and throw away the key? The only component that can justify the death penalty over life imprisonment is an emotive one: a kind of Biblical craving for "an eye for an eye". I don't agree with that view, but for many people that is the deciding factor.
I also don't agree at all with Cedille when he says "The biggest difference between death penalty and murder is the former is for a good cause". I've heard that argument a lot, but I don't understand how people who support it fail to see the logical flaw in it. If the deciding factor when it comes to killing someone is that it is for a "good cause", then what prevents people (like every two-bit psycho out there) from taking matters into their own hands and committing the "good kill" themselves? What gives the state a monopoly on the right to kill and the right to decide who should be killed and who shouldn't?
The primary reason I oppose the death penalty is that I do not want to entrust the state with the power to kill. Giving the state the power to execute people and then hoping they will always use that power "appropriately" (whatever that means) is just dumb. It always boggles my mind how even people who are critical of government meddling and overbearing bureaucracies somehow forget their reservations when the death penalty is involved. It clearly shows, I think, that they're not really thinking of the consequences for society or of any "justice", but rather want the state to act as an instrument of their thirst for revenge. Of course, when one reads stories as the one avatar! linked to, one can very much understand and sympathize with that standpoint (and to be sure, there have been much worse crimes committed than those). The problem is, as Jay pointed out, who decides who should live and die? Killing someone is irrevocable, and when the state has killed even one innocent person, it has basically lowered itself to the same level as the people who commit murder. And we all know there have been a lot of innocent people executed throughout history, and still are today. The justification for the death penalty rests on the most retarded argument in the history of mankind: "If you haven't done anything wrong, you have nothing to fear". If you trust the authorities with the power to kill, you should just bend over and be ready to take whatever else they want you to. And the sad truth about our world is that too many people do both.