I would hope that forensic science is advanced enough that guilt should be 100% proven before a death sentence was even considered a possible punishment?
You've not heard of police corruption then? Police who frame suspects, just because they want to get someone for the crime?
Not to mention miscarriages of justice.
The Innocence Project
Now the majority of people (mainly men, but there are a couple of women) cleared by the Innocent Project weren't sentenced to death, but some were (18 in fact, figure provided elsewhere on the site), but looking at all these names makes me wonder who many innocent men may have been executed. It can take years for these innocent people to be cleared, and for some on death row, the time probably runs out.
There aren't any concrete figures on how many innocents have been executed in the US, because American courts don't tend to entertain appeals of innocence after execution.
However, there are cases of people executed, where strong evidence exists of their innocence. The most recent of those was the abhorrent execution of Troy Davies in 2011.
It is estimated that one in 25 of the people sentenced to death in the US are actually innocent, and while that's clearly a minority, in my mind the execution of just one innocent is one too many.