The Old Testament Law prescribed the death penalty for an extensive list of crimes including:
Jesus said His mission was not to abolish the Law, but to fulfill it (Matthew 5:17-20). However, He and His apostles greatly modified our understanding of God's intentions. Love is the principle that must guide all our actions (Matthew 5:43-48, Mark 12:28-34, Luke 10:25-28, Romans 13:9-10, Galatians 5:14). Christians are bound by Jesus' commands to "Love the Lord your God" and "Love your neighbor as yourself" (Matthew 22:34-40). We are no longer bound by the harsh Old Testament Law (John 1:16-17, Romans 8:1-3, 1 Corinthians 9:20-21).
Related article: What Does the Bible Say About the Old Testament Law?
Jesus flatly rejected the Old Testament principle of taking equal revenge for a wrong done (Matthew 5:38-41, Luke 9:52-56). He also said that we are all sinners and do not have the right to pass judgment on one another (Matthew 7:1-5). In the case of a woman caught in adultery (a capital offense), Jesus said to those who wanted to stone her to death,
"Let anyone among you who is without sin be the first to throw a stone at her." And once again he bent down and wrote on the ground. When they heard it, they went away, one by one, beginning with the elders; and Jesus was left alone with the woman standing before him. Jesus straightened up and said to her, "Woman, where are they? Has no one condemned you?" She said, "No one, sir." And Jesus said, "Neither do I condemn you. Go your way, and from now on do not sin again." (NRSV, John 8:7-11)
The apostle Paul also warned against taking revenge for a wrong done (Romans 12:17-21, 1 Thessalonians 5:15). Likewise, the apostle Peter warned us not to repay evil with evil (1 Peter 3:9).
Some proponents of capital punishment see it as mandated by the Old Testament Law. However, Christians are no longer bound by the legal code of Old Testament Law. The argument of a Biblical mandate for capital punishment is also contradicted by the fact that many of the capital crimes in the Old Testament are considered relatively minor today. Very few people in the Christian world would support capital punishment for such things as doing work on the Sabbath, false prophecy or making false statements about a woman's virginity.
Many proponents of capital punishment interpret the phrase, "authority does not bear the sword in vain!" in Romans 13:1-5 as New Testament authority for capital punishment. However, the point of this passage is that Christians must not use their freedom from the Old Testament religious Law as an excuse to violate the civil law. We must obey civil authority, which is instituted by God, because of fear of punishment as well as conscience (verse 5).
Opponents of capital punishment see it as exactly the kind of revenge and human judgment that Jesus and His apostles so often warned against. They believe the principles set forth by Jesus and the apostles restrict punishment to only that which is necessary to protect society (i.e., humane confinement of offenders).
Opponents of capital punishment also point out that Jesus taught great principles for us to apply in our lives, rather than specific laws. Thus, his failure to specifically condemn slavery, capital punishment and many other evils should not be interpreted as approval of those things. They see the mercy He showed to the woman caught in adultery (John 8:3-11) as His rejection of capital punishment. However, Jesus never specifically repudiated capital punishment.
Some opponents of capital punishment see a prohibition against capital punishment in the Ten Commandments (Exodus 20:13, "Thou shalt not kill" in the King James Version). The original Hebrew word ratsach, translated as "kill" or "murder" could refer to either killing in general or unlawful killing (murder). However, most experts think this is not a prohibition against capital punishment because the death penalty is specifically authorized elsewhere in the Old Testament.
Here are the official position statements:
2267. Assuming that the guilty party's identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.
If, however, non-lethal means are sufficient to defend and protect people's safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity with the dignity of the human person.
Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm-without definitively taking away from him the possibility of redeeming himself-the cases in which the execution of the offender is an absolute necessity "are very rare, if not practically non-existent."
From Catechism of the Catholic Church, second edition, copyright © 1997, United States Catholic Conference, Inc., http://www.usccb.org/catechism/text/pt3sect2chpt2art5.htm
[A resolution adopted at the June, 2000 convention of The Southern Baptist Convention] affirms the use of capital punishment "by civil magistrates as a legitimate form of punishment for those guilty of murder or treasonous acts that result in death." The death penalty should be used only when there is "clear and overwhelming evidence of guilt," the proposal says. It also calls for "vigilance, justice and equity in the criminal justice system," with capital punishment "applied as justly and as fairly as possible without undue delay, without reference to the race, class or status of the guilty."
Basic Freedoms and Human Rights
We hold governments responsible for the protection of the rights of the people to free and fair elections and to the freedoms of speech, religion, assembly, communications media, and petition for redress of grievances without fear of reprisal; to the right to privacy; and to the guarantee of the rights to adequate food, clothing, shelter, education, and health care. The form and the leaders of all governments should be determined by exercise of the right to vote guaranteed to all adult citizens. We also strongly reject domestic surveillance and intimidation of political opponents by governments in power and all other misuses of elective or appointive offices. The use of detention and imprisonment for the harassment and elimination of political opponents or other dissidents violates fundamental human rights. Furthermore, the mistreatment or torture of persons by governments for any purpose violates Christian teaching and must be condemned and/or opposed by Christians and churches wherever and whenever it occurs. For the same reason, we oppose capital punishment and urge its elimination from all criminal codes.
- From The Book of Discipline of The United Methodist Church--2000, ¶164A. Copyright 2000 by The United Methodist Publishing House, http://www.umc.org/abouttheumc/policy/political/a-basicfreedoms.htm