1) vengeance is a raw, human emotion that is normal in family members of murder victims, but it can never be used to justify a public policy given that policies are supposed to be based on reason and empirical science.  Additionally, the state is technically/legally the victim when a crime occurs and is incapable of feeling vengeance.  A careful analysis of the entire Bible, taking the whole Bible in its historical context, does not provide a mandate for capital punishment, even for murderers.
 

2) retribution is a state sponsored, rational response to criminality that is justified given that the state is the victim when a crime occurs.  The government is justified in pursuing justice when it is harmed in order to re-balance the scales of justice that were tilted to the benefit of the offender when he or she broke the law.  In reality, however, the death penalty does not generally achieve retribution because it is so rarely applied to murderers (less than 2% of aggravated murderers are sentenced to death and FAR LESS than 1% of all killers are sentenced to death);
 

3) deterrence is the notion that by administering punishment to offenders, the state can cause fear in both the offender (special or specific deterrence) and in others (general deterrence) so that they will not want to commit crimes in the future.  Obviously, capital punishment cannot achieve special or specific deterrence because once the offender is dead, he or she cannot be afraid of future punishment.  The available scientific evidence with regard to general deterrence suggests that the death penalty is not a deterrent to murder and cannot be for the simple reason that the most important element of punishment is missing -- certainty.  Punishment must be certain in order to deter, whereas the administration of the death penalty is so rarely applied and so unlikely to be applied to any individual that to even suggest that the death penalty is a general deterrent is a very weak claim.

For more, see this page on deterrence.
 

4) incapacitation means taking away a person's freedom so that he or she cannot commit another crime.  The typical form of incapacitation is incarceration (in a jail, prison, etc.).  The ultimate form of incarceration is death.  As with retribution, this is a legitimate justification for the administration of punishment because the primary responsibility of government is to protect its citizens from harm, and one of the goals of our justice systems is to reduce criminality.  Unless you believe in reincarnation, you will agree that the death penalty achieves these objectives, but only for those few that we execute.  Like with retribution, we generally do not meet this objective simply for the fact that the death penalty is so rarely applied (less than 2% of aggravated murderers are sentenced to death and FAR LESS than 1% of all killers are sentenced to death).
 

The conclusion seems to be that we have some legitimate reasons to pursue the death penalty IN THEORY, but IN REALITY, we do not meet these above objectives.  In other words, the practice of capital punishment in the United States does not meet its goals.  We simply do not achieve the objectives we set out to achieve, thus a fair assessment of this policy is that it is not sustainable as currently practiced.
 

So, what are our options? .... I see two possibilities: 1) use capital punishment MORE or 2) DO NOT USE capital punishment at all.  Given the ruling by the U.S. Supreme Court in Woodson v. North Carolina (1976) that mandatory death for all murderers in not permissible, we cannot kill them all!  For more, see this page on the case.

So, how do we kill more in order to achieve our objectives?  Prosecutors do not seem willing to seek it, juries are unwilling to impose it, and states are unable to pay for it.

Of course, the fact that the death penalty does not meet its goals is only half of the story.   There are also alleged serious problems with the administration of the death penalty in the United States.  For more on these alleged problems, see this page on alleged problems with the death penalty.