The death penalty serves two important purposes, regardless of one's personal attitudes about it.
First, it normalizes killing in self defense. Countries that abolish the death penalty sooner or later abolish meaningful self defense. See Britain, for example.
Second, and this to some extent ties into the first purpose, it discourages vigilante "justice". See for example the high mortality rate of certain criminals in the prison system, such as pedophiles.
Those who believe in death penalties aren't going to decide somebody deserves to live just because the law says they can't be killed. The death penalty, and all the expensive appeals that come with it, is a necessity (insomuch as a justice system is a necessity at all; see my post Do Police Civilize Society) when the population wants it, regardless of one's personal attitudes towards it.
That said, I'd prefer the system be reformed to require a substantially higher measure of evidence than is currently the case. But I feel the same way about just about all the possible punishments.