The Guillotine and Capital Punishment

During the Reign of Terror of the French Revolution, 300,000 people were arrested.  Of those people, 17,000 were executed by the Guillotine.  Many of those who were executed were victims of mistaken identity, or were falsely accused by their neighbors.
Today, over 30 states in the U.S. (including the military and federal government) have the Death Penalty, or Capital Punishment as part of their State Laws.  Since 1976, there have been over 1,200 executions in America.
Do you believe the Death Penalty should still exist?  Why, or why not?  Consider possible innocent victims and consider mass murderers.  Give your reasons for or against Capital punishment.