I am against the Death Penalty simply because innocent people could be convicted and death is irreversible, but I fail to see what's wrong with revenge as a motive. When an innocent person has been harmed, either the victim or the victim's family is perfectly justified in seeking repayment in kind. We've simply accepted that that's "barbaric," in my opinion unquestioningly. However, if justice is about some degree of equalization (which I would argue it is), then punishment for punishment's sake isn't such a bad thing.
That said, the whole concept of a "debt to society" is ridiculous. The criminal has a debt to the victim and no one else. I just don't see what's morally wrong with demanding they pay that debt in some way--and by definition, that's pretty much revenge.
So in principle, I don't have much of a problem with the death penalty. It's certainly not any more "barbaric" than most of the crimes people are executed for. In reality, it is impractical and dangerous, but some other severe punishment as revenge is perfectly reasonable IMO. I just think the punishment is best determined by the victim or the victim's family rather than society at large (so long as they don't overstep their bounds)--but that would require overhauling the justice system entirely).