Incapacitation of the criminal.
Capital punishment permanently removes the worst criminals from society and should prove much safer for the rest of us than long term or permanent incarceration. It is self evident that dead criminals cannot commit any further crimes, either within prison or after escaping or after being released from it.
Cost.
Money is not an inexhaustible commodity and the government may very well better spend our (limited) resources on the old, the young and the sick etc., rather than on the long term imprisonment of murderers, rapists, etc.
Anti-capital punishment campaigners in the U.S. cite the higher cost of executing someone over life in prison, but this, whilst true for America, has to do with the endless appeals and delays in carrying out death sentences that are allowed under the U.S. legal system where the average time spent on death row is over 12 years. In Britain in the 20th century, the average time in the condemned cell was from 3 to 8 weeks and only one appeal was permitted.
Retribution.
Execution is a very real punishment rather than some form of "rehabilitative" treatment, the criminal is made to suffer in proportion to the offence. Although whether there is a place in a modern society for the old fashioned principal of "lex talens" (an eye for an eye), is a matter of personal opinion. Retribution is seen by many as an acceptable reason for the death penalty according to my survey results.
Deterrence.
Does the death penalty deter? It is hard to prove one way or the other because in most retentionist countries the number of people actually executed per year (as compared to those sentenced to death) is usually a very small proportion. It would, however, seem that in those countries (e.g. Singapore) which almost always carry out death sentences, there is far less serious crime. This tends to indicate that the death penalty is a deterrent, but only where execution is a virtual certainty. The death penalty is much more...