h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

That is, it wouldn't work if it were possible, which it isn't. And even if you did have it, you still couldn't ever get it to work.
Over a large group of people, such as the United States, or the whole world, or whatever society you want, there has to be a 'way things work' around here. Or there. Whatever. The Greeks, like the other person here said, didn't invent government. This is because there were people before them. The Egyptians had pharaohs. The mesopotamians had rulers as well. Even cavemen, ect. They had government. Basically, the person who had the most potential to kill somebody had the most power and made all of the rules. That's why animals on a farm will never dream of rebelling from the farmer, like in the book Animal Farm. This is because the farmer could kill any of those animals any time he felt like it by getting his rifle out. (also because the animals don't have powerful enough intellects to figure this sort of thing out, but that's beside the point)
Even if there were anarchy reigning the world, it simply wouldn't work. Several reasons for this exist. For instance, there would be absolutely no restrictions. None at all. If you wanted to blow up some neighbor's house, feel free to. Nobody's going to stop you unless they have spare explosives and guns lying around. You are always in danger at work because you could be killed by your workmates or some outside terrorist at any minute. No policemen or armies are going to stop them because they don't exist. You can't have order without standards, and these standards can only be set by the rulers, which don't exist in an anarchist world. Another reason is because there wouldn't be any motivation to work, and without that, nobody will be fed, everything will run out of stock, and millions will be homeless. Think about it: Money is legal tender. Legal tender is appointed only by a government or ruler. Without them, you can just go to the music store and pick up a few stereos, electric guitars, drumsets, basses, keyboards, grand pianos, and amplifiers without a penny leaving your pocket. Maybe this is a cool-sounding idea, but if this is the case, nobody will be motivated to work. You work partly because you enjoy it, maybe. But if there's no money involved, you'll stop working. Having fun's okay, but so is staying alive. Or doing anything worth doing.
I don't feel like listing other ideas. The point is, anarchy is a stupid idea that never can or will happen in anybody's lifetimes.

I partly agree, for, though I do believe that it is an attractive idea having so much freedom, and that having no government would be excellent, I have a problem with its reliance on the goodness of human nature. You can't rely on humans to be 'good' and to live in harmony bacause there will always be people who will cause trouble and will (as you say)kill and steal with no laws to stop them. The 'big' people will always pick on the 'small' people and people wont treat others as they expect to be treated.

It is a shame though...perhaps it would work on a very very small scale?