Death Sentence is a touchy subject and ranges across many aspects of thought and reasoning. Here are three to summarize:
Politically: Since America is based on the Liberty school of thought, in other words, the governments only responsibility is to protect the liberty and rights of the citizens, then an action that takes ultimate liberty, life, away from a person is wrong. It could even be argued that the framers of the constitution felt that the way a government transitions from benevolent to malevolent is when it takes liberty away from it's citizens. So as an action by government, I don't think it's right.
Religiously: Depends on the religion. I'm a very strict Christian and Christ told his followers to both love their neighbor and to not live by the sword. As a Christian, killing someone is DEFINITELY out of the question.
Pathos: This is emotion for those who don't know. When you hear about teenage girls being tortured, raped, and strangled to death, something wells within. From pure emotion, the death penalty may seem justified. I know if it were my daughter, that despite my Christian upbringing, not killing that person would be very difficult. I wouldn't do it, but I guarantee you I'd think about it.
Like I said in the other thread, the best way to handle such cases is to try and convict the individual, but leave the fate up to the victims (in this case the surviving family). They could decide based on their personal views which way to go. Such a solution assures Liberty for the family, respect for religious views, and takes into consideration their personal pathos.