I submit that the death penalty, if adopted as part of a well-designed justice system, can be a net positive influence. If, however, it is misapplied or applied as part of a misguided system, it becomes a strong negative influence.
In an extropic world the death penalty is, in a sense, an infinite punishment, since the defendant is robbed of a potentially eternal existence. Therefore it should never be an option for crimes that do not involve loss of life. For cases involving clearly accidental death it also seems inappropriate, even if some lesser crime was being committed at the time.
Even for actual murder cases, there are often extenuating circumstances. Many crimes are committed in a fit of passion, or by people who are incapable of understanding what they are doing. Each case would have to be examined individually, but in most cases lesser punishments seem more appropriate.
The cases where the death penalty is truly called for are those that polite society does not like to acknowledge. To put it bluntly: there are people out there who are perfectly willing to murder as many people as they need to in order to achieve their goals. They know exactly what they are doing, and they don't care. They have made a rational decision that their goal is more important than any number of human lives, and they are willing to act on that decision.
These are the people who should be executed. If you catch such a man and kill him, you are responsible for only one death. If you let him go, there will be dozens of deaths (in some cases hundreds, or even thousands - terrorists are a good example of this). Punishing him won't make him stop, it will simply make him more careful. Life imprisonment is impossible - we're talking about immortals here, right? Involuntary reprogramming simply makes you guilty of a different crime, and it leads inexorably to problems that are far worse than a few mass murderers. Since there don't seem to be any other alternatives, I think execution is the only viable option.