Against it, myself. I used to be for it just because I was raised conservative, but about a year and a half ago I did a term paper on it. This, of course, involved researching both sides using multiple sources. Basically, in my opinion, yes, capital punishment does have its place, but not in the United States (my research focused on the US).
Concerning justice, well, there are moral arguments against that. For instance, it is not man's place to judge. The correct purpose for a 'justice' system is to protect society from individuals who would cause significant harm (which is determined by legislation passing laws). Yes, God can use courts to bring justice, but such an occurrence is determined by Him, not men; it is arrogant (imo) to think that everything men call "justice" really is justice, especially considering that God has made it perfectly clear that He is willing to allow our volition to get in the way of what may be good, right, or just.
As for deterring crime, capital punishment is not much of a deterrent. The arguments for this are largely statistical, but the problem basically comes down to how people perceive capital punishment. It does not apply to most crimes, it will not necessarily be given in cases which may allow it, it is decided in the distant future (when the trial comes around), and it is enacted well past that (after all of the appeals). Besides, when a person is committing a crime normally deemed as deserving death, they are very rarely concerned at all about what will happen to them afterwards, causing the chance of being deterred by the risk of capital punishment to fly out the window. As for making capital punishment public, which would honestly fix the above problems for the most part, that will never happen in the US. Way too many people would be opposed.
I will now elaborate on the two main reasons against capital punishment.
First, capital punishment is costly. A very, very significant amount of money goes into getting permission to kill a convicted person. I don't have numbers on me, but I am sure you can look it up if you want to. Basically, the costs of the appeals come mostly out of the public's pockets. Those on death row will attempt as many appeals as they are allowed, since it pushes back their execution. If capital punishment were done away with (which I don't think will have much detriment, for the reasons I mentioned above), that money could be sent to better purposes. Yes, there have been cases of convicted criminals getting out and murdering people, but if the money is spent right, it can save many, many more. And if you think we should do away with the appeals process and just execute people right away, there is a problem with that because:
Second, not everyone convicted of a crime is guilty. In those appeals, people on death row have actually proven their innocence (yes, proven, in the same sense that their guilt was proven). The quicker the executions are carried out, the more innocent people who will be killed. No, imprisonment isn't perfect in this regard, it also takes away from an innocent person's life.. but at least, if they are innocent, they have a chance at regaining part of what's left of that life.
Idealistically, of course, capital punishment wouldn't be needed. And, speaking practically, I cannot be entirely sure that I am right in opposing it for the US. However, based on what I do know, I do think it would be better to do away with it than leave it as it is. Feel free to disagree, of course. These are just my opinions.