I've talked to many people who believe that the inherent danger of executing an innocent person is the most compelling reason to abolish the death penalty. In response, death penalty proponents often argue that the system has sufficient protections built in to ensure this won't happen and that there has never been conclusive proof that an innocent person has actually been executed. Justice Scalia made this argument in his concurring opinion in Kansas v. Marsh, 548 U.S. 163 (2006): "It should be noted at the outset that the dissent does not discuss a single case—not one—in which it is clear that a person was executed for a crime he did not commit. If such an event had occurred in recent years, we would not have to hunt for it; the innocent’s name would be shouted from the rooftops by the abolition lobby."
Here's my shout from a laptop: Cameron Todd Willingham
The latest New Yorker has a well-documented article providing as-conclusive-as-you-can-get proof that Cameron Todd Willingham, who was executed by the State of Texas in February 2004, was factually innocent. The main (but certainly not only) flaw in the evidence was that expert testimony that the fire was an arson was based on "junk science" with no scientific validity. According to the New Yorker piece, the country's foremost fire investigator Dr. Gerald Hurst's conclusion that the fire that killed Willingham's three girls was an accident has since been confirmed by multiple top fire investigators, including one hired by a Texas commission to investigate allegations of error and misconduct by forensic scientists. For a more in-depth discussion of the illingham case, see "Trial By Fire: Did Texas Execute An Innocent Man?," New Yorker, 9/7/09. For those who prefer an audio summary, check out NYer Podcast with Author David Grann