Yes, for certain crimes like being president of the USA.
No. The Death Penalty has proven itself not to work, and against someone like me* its possibility would be the worst possible idea. It's a much better idea to simply remove them from society, break up any "social groups" that exist inside the gaols and try to rehabilitate.
* If, after having committed a crime that carries the possibility of the death penalty, someone like myself might just say "well fuck it, if i'm going to die, i'm going to die taking EVERYONE out", and then proceed to installing bombs in primary schools, putting nerve gas in public institution air conditioners, and just generally massacre a lot of people.