Personally I think we could do without a person like Breivik. It will not prevent another person from doing a similar act, but it prevents HIM from doing the act again. After all, violent offenders are highly likely to do it again. Recidivism is a thing. When the crime is of particularly abhorrent type, like mass-murder, child rape and such, the perpetrator should always be considered eligible for the death penalty and by eligible I mean that it should never be doled out lightly.
Take Breivik as an example again. What he did showed planning and cold-bloodedness, he never has shown any remorse and the reasons he himself has given show a deeply faulted view of life in general. Purge him from the human existence.