To get this forum started, an old favourite:do you support the Death Penalty? For the moment, let's assume just for murder.
In my case, no. Let's start with the fact that if you still execute people you are in the select company of such countries as Iran, China and Saudi Arabia.
Next, it's not a deterrent, if that's your justification. It never has been. This should be obvious when you think about the types of murder. Most murders are almost spontaneous. They are crimes of "passion" between two people who know each other, probably well. The intention to kill was formed only seconds before the crime took place, so the murderer has no time to think of the penalty. Next up are multiple murderers. Like most people who take their time over murder, they don't think: "if I get get caught I will be executed", they think: "If I do X and Y I won't be caught." You can't deter a person who doesn't think they will be detected. And finally we have fanatics who simply don't care if they are executed - they may even welcome it.
But at the bottom is the moral question: if they state says it wrong to kill, why is it OK for the state to do so? Aren't you just lowering yourself to the level of the murderer?