From the Death Penalty Information Center:
Georgia death row inmate Troy Davis was scheduled to be executed numerous times in 2008, but each date was stayed. His case is currently under review by the U.S. Court of Appeals for the 11th Circuit. International interest has continued to mount because of concerns about his possible innocence. Most recently, Amnesty International has assisted in preparing a multimedia presentation about his case with the music group "State Radio."... Davis’ case has garnered support from many quarters, including former President Jimmy Carter and the European Union. Davis' original conviction was based primarily on eyewitness testimony. Since the 1991 trial, 7 of the 9 non-police eyewitnesses have recanted their testimony, with some pointing to another suspect.
The mind-boggling aspect of Davis' case is that, even though 7 of the 9 eyewitnesses have recanted – leaving good reason to believe that the remaining two are also mistaken – that's not enough to constitute sufficient grounds for the vacation of his conviction. Instead, he's had his execution stayed several times by the court, rather than simply give him a new trial whose result would reflect what we know today. The state has fought tooth and nail to preserve Davis' conviction, seemingly because they're afraid of what a new trial would show.