There is good evidence that Texas executed an innocent man in 2004. Cameron Todd Willingham was convicted of burning his 3 children although the only evidence was testimony from arson investigators that has since been completed refuted by more modern and knowledgeable experts. The New Yorker article is a must read.

In a scathing report, he concluded that investigators in the Willingham case had no scientific basis for claiming that the fire was arson, ignored evidence that contradicted their theory, had no comprehension of flashover and fire dynamics, relied on discredited folklore, and failed to eliminate potential accidental or alternative causes of the fire. He said that Vasquez's approach seemed to deny “rational reasoning” and was more “characteristic of mystics or psychics.” What's more, Beyler determined that the investigation violated, as he put it to me, “not only the standards of today but even of the time period.”

... Just before Willingham received the lethal injection, he was asked if he had any last words. He said, “The only statement I want to make is that I am an innocent man convicted of a crime I did not commit. I have been persecuted for twelve years for something I did not do. From God's dust I came and to dust I will return, so the Earth shall become my throne.”