I've been all over the place on this one.
In college I had no objection to the death penalty per se on moral grounds, though I was bothered by the possibility that innocent people could be executed. So I was against the death penalty in its current form, but would have supported a system that would reduce to near zero the probability of executing an innocent person. I had in mind something like an expanded list of capital crimes with a requirement that, in order to be subject to capital punishment, a person would have to be found guilty and deserving of the death penalty for three such crimes committed at different times.
Then I was briefly against the death penalty on the grounds that murder is murder - whether committed by individuals of the state. That argument fell apart when I accepted that there can be such a thing as 'just war' in which people die and so the State may sometimes be able to commit morally sanctioned homicide.
The defining experience for me grew out of some work I was encouraged to do with death row inmates. (When I lived in London, I worked with the Samaritans as a counselor. When I moved to NYC my schedule didn't allow me commit to the hours needed to be a counselor, but I was put in touch with Befriender's International, which, among other things, organizes pen pals for death row prisoners.
I have learned much from this experience. First, that people can change. The three prisoners with whom I have corresponded undoubtedly committed heinous crimes - many years ago. But I have complete confidence that two out of the three are fundamentally changed men. They understand what they did, are deeply remorseful (and always will be) and make no argument that they should be spared punishment (such as permanent incarceration). The third is younger and has not accepted his responsibility for what he did, but I believe that in time he will.
I have also seen that living with a death sentence is a form of slow torture. Two of the three prisoners I have worked with have come very close to execution on more than one occasion - only to receive stays.
No doubt incarceration (especially in maximum security facilities) is very expensive in financial terms, but so is the death penalty. And abandonment of the death penalty in favor of life imprisonment allows us to avoid the possibility of executing the innocent, having to live with the clear inequities of who gets executed (usually poor people and especially poor black people). Most importantly, it allows us to remain true to the belief that with time and reflection people can change and,even behind bars, find some meaning in their life and maybe even contribute to the benefit of others.