Responding to crime and tragedy is always difficult, and the first step is empathy for those who have suffered most, the victims. That, however, is independent of how we deal with the criminal. There, the first question is the mental status of the criminal-- certainly not all evildoers are insane, but some are, and we should be careful not to ignore that possiblity. In Jewish law, the insane have a different status than the sane, and are less culpable for their actions. That does not mean insanity is a free pass, but it changes the nature of the incident-- if a crazy man shoots up a mall, we have the same sadness for the victims, but would view it differently than if an evil person did the same thing to make a political point.
In the case where we conclude the criminal was, in fact, sane enough to be liable for his/her actions, our first responsibility as a society is to respond to the evil in ways that make clear our rejection of such actions. The Torah several times speaks of being meva-er, eradicating, either evil or spilled blood, from our midst. We, as a society, must make clear that such acts are completely unacceptable and that we will combat them-- and try to prevent them-- to the best of our abilities.
That said, we have concern and compassion for the criminal as well. Even if the person is not technically insane, it is likely that there are many psychological components to this person's evil, and that will affect how we react to it. There is also the question of remorse-- the Talmud notes that once an evildoer (of a lower level than murder) receives punishment, s/he returns to being our full brethren. The assumption is that crime, with punishment, restores the person to his/her ordinary state. So, too, I would differentiate between those who have remorse and those who don't. It is not a question of forgiveness-- which is up to God, not us-- it is a question of at what point we feel comfortable restoring this person to ordinary citizenhood. For some crimes, the answer might be never (such as murder, etc., for which the Torah assumes the death penalty and we in America might assume life in prison).
So the question with criminals isn't whether we forgive them; it's when we accept them back into society, restore them to ordinary citizenship, and that is a case by case question.
Answered by: Rabbi Gidon Rothstein