I'd prefer to use those on death row as entertainment a la gladiator style or 'Running Man', otherwise, yes on executions for serial killers and murderers who are proud of their crimes, or would clearly do it again. Some people you just need to put down as rabid animals.
In regards to justice, I advocate at least 'an eye for an eye' or 'a tooth for a tooth' for malicious acts. Perhaps even 'two teeth for a tooth', so that which was taken away by the perpetrator will be taken away from him.
If someone steals money or property worth whatever value, it's not enough to just take it back and give it back to the victim, plus pain and suffering, etc, to make the victim 'whole'. Since the offender has deprived the property of the victim, perhaps the offender must be deprived of the same amount of property and granted to the victim in addition to what was stolen and also for 'pain and suffering', inconvenience, lost wages, lawyer fees, etc.
If the offender can't pay, then he gets put to indentured servitude to work that amount off to make restitution.
If the offender raped someone, he gets raped, twice over, if the victim desires. Perhaps by a hired professional rapist - who knows. If he cut off someone's finger, he gets two fingers cut off by the victim, or by someone the victim specifies (the government, a defense agency, a professional of some sort, etc).
It wouldn't be perfect, and there would be some instances where people can't be truly made 'whole', but it would be a helluva lot better than what we have now, IMO. Of course, the victim would have the option of forgiveness, as well - but he could require restitution or punishment *up to* the 'two teeth for a tooth' rule.