"'The man who commits adultery with another man's wife, he who commits adultery with his neighbor's wife, the adulterer and the adulteress, shall surely be put to death." - Leviticus 20:10
This is only one of many examples of laws in the Old Testament that condemn people to death for crimes. So then the question arises:
"If it's in the Bible, and Christians believe the Bible to be the final authority over their lives, then why don't Christians put adulterers to death? Isn't that picking and choosing which parts of the Bible they want to believe?"
This is an excellent question, and it often comes up as an argument against Christianity when I'm talking to people. Surprisingly, the answer is very simple:
What was the punishment for sinning before Christ? Death.
What was it that Christ did to take the punishment for sin upon Himself? Died.
Usually when I tell people that, they'll quote Jesus in Matthew 5:17:
"Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill."
There you go. Jesus said it Himself! We aren't supposed to get rid of the law, we're supposed to uphold it! Or are we?
Think about this for a second. If there was no law given, would we understand the reason Jesus came to die for us? No, because without the law, we wouldn't know we were breaking it and therefore not know we were sinners. So no, He didn't come to destroy it. But He didn't say He came to establish it either. He said He came to fulfill it.
What is the fulfillment of the law?
"For the commandments, "You shall not commit adultery," "You shall not murder," "You shall not steal," "You shall not bear false witness," "You shall not covet," and if there is any other commandment, are all summed up in this saying, namely, "You shall love your neighbor as yourself."
Love does no harm to a neighbor; therefore love is the fulfillment of the law." - Romans 13: 9-10
Love is the fulfillment of the law. Jesus loved us, came to pay the punishment of our own sins by dying for us because of His love for us, therefore fulfilling the law, just as He said He came to do.
So why don't Christians put these people to death, or carry out the punishment of the laws according to the Bible? Because Christ already fulfilled the law for us, making us no longer under the law.
This is not a license to sin though (Romans 6:1-2). Anyone who is in love with their sin is against Christ, because Christ is against sin. Anyone who is dead to sin is alive to Christ, justified by His sacrifice. Only those who are dead to sin could be trusted with not being under the law.