Victims, and the families of victims, have a strong emotional need for vengeance. Maybe they shouldn't, but they do, nonetheless. If government does carry out justice, then people will take it in their own hands. "Justice" is when vengeance is handled in a impartial and fair manner--that is, when all possible efforts are made to ensure the person punished is indeed guilty, and to make sure the punishment is not out of proportion to the crime.
I've never really accepted Ian's idea that mere ostracism is sufficient to deal with those who commit heinous crimes. O. J. Simpson, a known murderer, got off scot free. He's subject to ostracism, but somehow, I don't think it's crimped his life all that much. He's never going to miss a meal, and manages to get his 18-holes in whenever he wants to.