It depends. I support it, but only for heinous crimes. Predisposed killing, rape, physical-harm paedophilia. I don't believe an accidental killing should be treated the same way as one you plan. After all, if I punch somebody the wrong way, I could kill them. That's not the same as picking up a knife and going people-hunting. Similarly (and controversially) there are different forms of paedophilia. If you rape a child then yeah, your life means nothing to me. But just staring at photographs on a computer? I don't feel it's the same thing.
However, the death penalty is not an exact science. We already know that there are people in prison right now, for crimes they did not commit. We have seen people unjustly imprisoned, and released five, ten, fifteen years down the line. Now imagine if those people had been put to death, only to later find them innocent. How can you atone for that?
So, I only believe in the death penalty when there is no doubt whatsoever. Everything must be scrutinized. For if just one innocent falls victim to the penalty, the system can no longer be considered just.