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Anarchy is a state of non-government that only exists while nobody is looking, similar to a vandalized page on Wikipedia or Schrödinger's cat while it's in the box. As soon as someone says "hey, let's do this" it isn't anarchy anymore. Obviously it isn't that great an idea; people who advocate anarchy are usually political children who are simply angry at the system and long for that brief amount of time, ranging from hours to days, when nobody will give them any orders.
There are, however, anarchists, a group of people who support anarchism. It must be stressed that anarchism is different from anarchy. Anarchism is a political philosophy in which large assemblies, assisted by committees, would use their power to ensure that nobody is able to wield power over others. (source: Anarchism FAQ) These anarchists are not opposed to apparent oxymorons such as anarchist organizations or an "anarchy logo."
Anarchists are often extremely angry at the prospect of anarcho-capitalism, a system similar to today's nation-states except on a much smaller scale. In a regular old anarchist government, it is okay to rob people or knock down their houses. You will be frowned upon but they won't imprison you. Anarcho-capitalists, on the other hand, would enter into Lockian agreements with their governments to guarantee their rights and security. It's not clear how an anarchist society would stop you from doing that, but it's just wrong.