Unsurprisingly for TSR, this debate is overwhelming influenced by Left-wing illogicality.
One of the fundamental maxims of justice and fairness in life is 'an eye for an eye'. If someone voluntary takes the life of another, without any lawful justification for doing so, I see no reason why that person shouldn't pay for that unlawful act with his life - ie, a life for a life.
To say that another course of action is 'fairer' or more 'just' is to spit in the face of reason: how can it be either fair or just for society to provide shelter, regular meals and - if the European bureaucrats get their way - suffrage to those who have so gravely wronged it?
The death penalty exists in some jurisdictions, theoretically if (supposedly) not in practice, to act as a deterrent; but it also performs a moral function insofar as it rectifies a previous wrong.
Those who say that there is a risk that an innocent person may be executed are, of course, correct; however, this is an infinitesimally small risk - especially in light of modern day technology. Furthermore, this argument falls down when one realises the prison sentence thus served would be equally unjust inasmuch as the person concerned has lost many years of his life.
Likewise, those who say that the death penalty is murder 'by a different name' fail to grasp the fact that in the absence of capital punishment, society implies that the gravest punishment one faces upon committing murder is incarceration for life - paid for by society: that is, the crime-punishment balance is not evenly weighted. I believe this is simply hopeless. An eye for an eye is the only pure form of justice and society should seek to impose that.