My wife did a lot of research on this topic for her college classes. One problem with the death penalty is that it does not prevent the crimes for which it is the punishment. Another, is that it costs around twice as much to put a prisoner to death, as it does to lock them up for life. And third, putting someone to death for a crime has nothing to do with justice. Justice is not supposed to be based on emotion, and executing someone is all about the revenge. Also, we are one of the few, if not the only, modern nation that still uses it.
Oh, and one more thing. I know a lot of the people who support the death penalty, are Christian, so how is it, that a Christian, who believes in the Ten Commandments, (i.e. Thou Shalt Not Kill), can condone the death penatly?