This is a great question and something that is very controversial. On the one hand it is sad to see anyone put to death. However, I think capital punishment is necessary. But it must be stated that there has to be no shadow of doubt that the person is guilty and deserving. All of this might sound harsh, but my rationale is twofold.
First, we live in a world where there are injustices. As awful as this sounds, it is true. There are those who seek to harm people and they must be stopped. The classic example is Hitler. People like him deserve capital punishment. Also think of the genocides even in our world today. A strong case can be made that we are not morally progressing.
Second, if we look at this question from a sociological point of view, we will see that it is only in liberal places (generally speaking) that this is even an issue. Justice requires capital punishment in their logic, not because life is cheap, but because it is the most important thing on earth. In other words, those who seek to harm others deserve a form of justice. At times, this is capital punishment.