http://www.deathpenaltyinfo.org/innocence-list-those-freed-death-row
This is a list of just the known instances. Certainly there have been plenty more, especially before DNA came into play.
I don’t trust my government with the most menial and simple tasks, why would I trust them on matters of life and death?
Hurricane Carter was "freed from death row" and is as guilty as hell. As Bill Ayers described himself, "Guilty as Hell and free as a bird. What a country!" "Freed from death row" is hardly the same as innocent. I doubt if even one percent of the people on that list are actually innocent in any meaningful sense, other than legalistically.
As Margret Thatcher (and I am sure others) have observed, when the government becomes involved in things it should not do, it does them poorly, and the incompetence spills over to larger things it should be doing. Maintenance of the peace is the prime charge of government, protecting the weak from predators, and punishing wrong doers. The most effective way of maintaining the peace is to insure that those that breach it are quickly and severely punished.
As a society, we have lost the stomach to punish evil. Prisons do not deter, the death penalty, as administered is a bad joke.