Christians are split on whether or not there should be a death penalty. Most mainline Protestant denominations oppose the death penalty. The Roman Catholic Church is opposed to it except for extraordinary circumstances, and the Eastern Orthodox churches have a similarly nuanced view. Fundamentalists and most conservative Protestants generally support the death penalty.
It seems that one’s view of the death penalty flows from one’s overall view of the Bible. If all books of the Old and New Testaments are equally the inerrant Word of God, and that one needs to look at the entire Bible to draw a valid conclusion. From this perspective, capital punishment is just, because the large number of verses in favor of it (with the only unambiguous ones being in the Old Testament) outnumber the small number against it.
I lean towards the alternative view (which I discuss at length here) that some Old Testament themes do not have a divine origin, and that the New Testament (especially the words of Jesus) can be used to interpret which is which. The most pertinent comments from Jesus on capital punishment come in the case of the adulteress, who is about to be stoned under the Law of the Old Testament. Jesus tells the crowd “He who is without sin among you, let him throw a stone at her first.” When no one comes forward, He tells the woman, “Neither do I condemn you; go andsin no more.” This is in keeping with the character of Jesus revealed throughout the Gospels, just as His replacing the maxim “eye for an eye” with “turn the other cheek”. It’s also worth noting that Jesus was Himself an innocent victim of capital punishment, wrongfully convicted.
I am personally opposed to capital punishment because I think it tends to bring out the worst in people, and because any errors made in its application are irreversible. However, I think it is a mistake for churches to be taking public policy stands at all, and I think Christian voters should be free to take either side of this issue. Jesus does not call us to establish either an “Old Testament style” theocracy, nor does He claim that His maxims about personal non-violence, compassion, and forgiveness are to be translated into public policy. Instead, He stands above the political fray. He makes clear that His kingdom is “not of this world” and that we should “give to Caesar the things that are Caesar’s, and give to God the things that are God’s“. It should be kept in mind that His message was addressed to vast numbers of people throughout history with no say in government policy at all, and that even the modern-day voter has a very low likelihood of swinging an election.