My position on the death penalty has changed. There was a time when I used to support the death penalty (not that this means anything, because I once thought drugs should be illegal, I had a lot of foolish ideas back then).
The standard argument against the death penalty has been the moral argument. It is immoral to kill other people, other than in self-defense, therefore the death penalty is immoral since it is not done in self-defense but for revenge. But somehow this argument never got to me. I never been moved by this argument. I always thought about Adolf Hitler or Joseph Stalin. I considered what would happen if these people were sentenced to death. Would I be crying my eyes out for them? No. It would not bother me if these people got executed. Even though I agree that these people should be killed, because it does not achieve anything, I am still not moved by the moral argument.
The other common argument used against the death sentence is that the death penalty is too expensive. This is the argument David Friedman uses against the death penalty on his blog here. But I do not like Friedman's argument. Friedman generally approaches these sorts of questions from a purely economic point-of-view by just comparing cost vs benefits. Friedman seems to agree that if the death penalty is actually cheaper than imprisonment then it should be used instead over imprisonment. So Friedman does not really take a stance on this issue, he simply only cares about the cost associated with killing and imprisoning.
The most persuasive argument against the death penalty that I heard came from TheAmazingAtheist in a YouTube video. Strangely he did not even use this as an argument against the death penalty. He pointed to the hypocrisy of conservatives who say that the government should stay out of the market but have no problem with the government staying in the business of deciding who should be executed, that is real "limited government" for you.
The main argument that I take now is a variation of what was said above. The state should not have the power to execute other people. Because that is giving the state too much power. The only kind of execution that I support is voluntary capital punishment. That is to say, if the criminal decides to be executed rather than imprisoned then he can choose this option. But if the state can decide for people who lives and who dies then this is giving the state too much power. I do not think the state can have this kind of power. And therefore, I do not support capital punishment.
Now I do have one more argument against capital punishment. I do not think anyone ever used this argument before. I call this the philosophical objection to the death penalty. The state is supposed to represent the delegated rights of the people. Of course, in all actuality this is non-sense. There is no consent of the people. There is no "non-consent of the governed". The social contract is a myth. The state does things that people cannot do themselves. And so forth. But ideally the state is supposed to simply be that institution that represents the people and it has its rights only from the delegated rights from the people. Do people have the right to execute other people? No. People have the right to self-defense, but people do not have the right to execute others. But if so then how can people delegate this right to the state? If people have no right to execute then how can they delegate this right? How can someone delegate a right they do not have? Thus, the state cannot have the delegated right to execute people.
If you are interested, Penn and Teller did an episode on capital punishment: here