Where did the idea of the death penalty come from?

The idea of death being a fitting penalty for certain offenses is older than recorded history. It's not even unique to humans: animals such as dolphins and dogs will drive away, deny food to, and even attack ostracized members of their group.

Hammurabi's Code, dating back to around 1700 BCE, contains several examples, including this passage: If a builder builds a house for someone, and does not construct it properly, and the house which he built falls in and kills its owner, then the builder shall be put to death.

Even The Bible has Matthew 5:38, the famous line about an eye for an eye, which is often used as a justification that the punishment should fit the crime.

In the modern era, the idea of a relatively humane death for certain crimes can be traced back to the development of the guillotine in 1791; followed by the 1872 invention of long-drop hanging, which snapped the neck instantly rather than causing death by slow strangulation. Of course, this eventually led to the development of lynch mobs -- but also to the idea of even more humane forms of execution, including the electric chair (1890) and lethal injection (1982).