ABSOLUTELY. That is, if we can be 100% sure of guilt. So, my answer is assuming it is absolutely known that the one to be executed is guilty.
I especially support it as punishment for the unlawful taking of the life of another. I often hear people say that a murderer is reformed, however, the person he murdered doesn't have the opportunity to reform.. or even breathe. I think that society should stress that life is precious and that the penalty for unjustifiably taking a life will be the death penalty. It's not fair for one to be able to take another person's life and then get to continue to exist - even in prison. Even in prison, one can eat, sleep, think, read, hope, enjoy life to some extent. His victim can't. He should not be better off than his victim.
And if he does not get the death penalty, he should never, ever, be released from prison, no mater how much he reforms and is sorry.... unless he can bring his victim back from death.