A very excellent question. I think often the crime doesn't warrant execution, those people we lock up.
Although, if you'd rather we didn't have incarceration, would you rather that the rapists, murderers, drug dealers and such, bought next door to you?
Or perhaps we simply said 'bad dog' swatted them on the head with a newspaper and told them not to do it again?
Or... we spend hundreds of thousands on attempted rehabilitation when often these thought patterns were formed before they learned right and wrong. These people who've done these crimes since they were pre-teens and continue to do so until they die.
Or we could just spend about $.50, and a pine box.