A lot of people on both sides of the death penalty overemphasise deterrence as a factor for or against execution. It is undeniable however, that the death penalty has a flawless 0% recidivism rate, which is more than can be said for any other punishment ever given out by any judge in any legal system in the world.
Here in Britain, there have been many instances of murderers released on parole from life sentences who have gone on to kill again. Even in America, where life often means life without possibility for parole, some lifers have gone on to murder prison guards and other inmates, and the most they can do is send them to the hole for a few months. The death penalty is if nothing else, the most practical way of removing a dangerous offender from society permanently.
My post # 18 lists some other reasons the death penalty does more harm than good.