I support the death penalty for a couple of scenarios. But Ultimately I think we need to rethink our use of it and prison in general. Namely because I don't like the definition we use for the penal system.
Here's the way my brain works. Prison, and the death penalty are all about removing people from our society that don't fit in with the established way our society works. But we approach the penalty as a punishment for a crime, not as a solution to the problem.
The way I think it should work, at least at some point, is really more of a three stage system based on the severity of the infraction and the plausibility of reintegration into society of the individual. For instance, robbery (or other first offense crimes) should probably continue to be a crime where prison/rehabilitation is the solution. But then we get into territory where I think the system does not work because we can only re-incarcerate someone for repeat offense, or a failure to reintegrate into society. So repeat offenders or offenders with more severe infractions just keep coming back. This is where I would put in an intermediary step between incarceration and execution for very serious crimes (murder, rape, manslaughter, things like that). I would do what the British did, and send them away from our society. Preferably to somewhere like Somalia where there is no acting government to reject the person. Thus avoiding the problem of offending people by state execution or allowing them to become a burden on society by paying for them to be in prison or returning them to society where they can offend again.
As for execution, I think it needs to be kept around for some scenarios. An offender who simply lacks the ability to be changed. Someone truly deranged or insane. Someone like charles manson or some truly sick sociopath. Someone who doesn't just not fit with our society, but does not fit with humanity at large, a war criminal, a monster.