This topic is really interesting and it can certainly raise some serious arguments.
Overall, i think that our legal system should be damped as it is not working in a fair way and most of the times, it is not even effective, meaning that criminals are not punished or punished equally to the crime they committed. I'm sorry to say that but even justice doesn't treat all thieves the same, all murderers the same etc. I have heard of people who killed others having a tv and other luxuries inside their cell, whereas people who stole lived under horrible circumstances, though killing someone is obviously much worse than stealing something.
Something else i never understood. How can we speak of life penalty, when it is only 20 years of prison? You can kill someone and if you behave well you may get out in less than two decades. Or even worse, pretend you have a psychological problem (if you are strong enough) and escape prison this way. This doesn't seem reasonable to me.
About death penalty, i can't say i'm pro or against it. It is not a decision i can make when sociologists and others have not decided yet if it should be banned or not. If it is a mass murderer we're dealing with or a molester just like Polandbaby16's example, death seems the only fair price to pay. But, is death really a punishment from them? I can't be sure.. What's for sure is that by killing these people we prevent other possible murders.
However, there is also the other side of the coin. When the government decides to kill someone, *technically* it accepts that killing a person can be legal under certain circumstances. Plus, we're talking about a country killing its citizens, which sounds weird enough. But i'm on the outside, and i know that if i had to deal with a murderer who hurt a person i love, i would probably want to see them dead. But still, human nature can act in very strange ways.
A movie i want to suggest on death penalty is David Gale's life. It might have been suggested already. But it is a great movie that will put you in lots of thinking.
Alright, that's it for real world. I could write more but this post has to end somewhere!
Ok, wizards. I agree as well that the magical world (if we can say that) is afraid of criminals since they are more powerful than Muggles. They can kill someone without even touching them. However, again, it is not fair convicting someone without taking them to the court were all evidence can be examined. However, still, it is hard to be sure that one has or has not committed a crime. We've already seen Voldemort altering his grandpa's (or uncle's, not sure

) memories so as to make him seem guilty. And although Dumbledore extracted these memories from him, it took a lot of time, exhaustion and great skills. But i think it would be worth it to have professional investigators who could be like Aurors who trace not criminals but clues.
Another argument i think no one has pointed out, is that all criminals are dealt with the same way. Sirius would be treated the same with a common thief. And though we know that he was innocent, he was believed to be a murderer. This is not fair. Why should someone who has robbed someone or broken into a house, be treated the same way as a murderer and suffer Dementors, which is a torture itself? Maybe they should develop a different system of punishing people according to the significance of the committed crime.
Last but not least, Dementor's kiss. To me, it is more horrible than killing a person. Cause this means he would have to live for long without actually living. Walking around like zombies, something like the guys in Invasion movie (have not seen it yet but that's the impression the trailer caused to me). It is the worst penalty ever. And especially expecting it. Cause you will not be really dead but you won't be able to live either. "Hell doesn't want him, heaven won't take him" or something. I am against Dementors as well. These creatures have nothing to do with humans and by giving them pain, we feed them and grow the evil hidden inside of them. There is no reason to do that...
So,I am against both systems, though ours seems more appropriate and lenient. I think there are huge changes to make but if we take it seriously, maybe one day our legal system will not only punish the way it should criminals, but also, be able to prevent people from committing a crime, of any sort.
Alkisti