For me it's not about deterrence and it's not about revenge. It's about justice. A person who takes someone's life should pay with their own. That's justice.
Studies that compare homicide rates in states with and without the death penalty are inherently flawed in that they tend to ignore other demographics of the particular states such as population density, median income levels, education levels, etc. A state with a large number of people living well below the poverty line will more likely have more crime including homicides. A state with large cities will have more crime than a sparsely populated state.
I know from a personal standpoint that the death penalty is a deterrent in some instances. There have been many times that I've thought about just driving right over some numbskull who cut me off or did something else incredibly stupid, but didn't because I couldn't remember if the state I was in was a death penalty state or not.