Someone raised this issue a few pages back. I started writing a quick response which turned into a long response and which is now my first diary posting. Things changed, evolved, and I adapted. Now THATs ararchy for you.
Anarchism encompasses a wide variety of opinions and positions. It encompasses the Anarcha-Feminism, anarcho-syndaclism (my personal fave), eco-anarchism, left and right wing anarchism, primitivism and many others. What I say here does not apply across the board, fair warning.
Anarchism is often misrepresented as being synonymous with chaos or disorder. This is a false assumption, based on a less then cursary glance at facts avilable. Anarchism can best be explained as a repudiation of Hierarchy. That is to say, it opposes inequal distribution of political power. What it proposes to replace it depends on who you are talking to.
I myself fall into the anarcho-syndaclist camp. I was raised by socialists, I cant help it. Im a "One World, One Union" type of guy. Yes, a Wobblie born out of time. How this translates on the ground depends on who you talk to. Some anarchists propose a version of the federal system, with small scale states seeing to their own affairs. This was originally the position of the Basque sepretists in Spain during the Spanish Civil War, before they were brutally crushed by the facists. Their position has since dengeneraded into ethnic sepratism, but a look at their early history would be quite enlightening.
As a male, I wont presume to speak for Anarcha-Feminism. It is my observation thouth that it seeks the challenge the obvious hierarchy of the patriarchy. I guess you could call the patriarchy one of the "big bads" to borrow from Buffy: The Vampire Slayer parlance. The military-industrial complex may be very destructive, but it hasnt had 4000 years to wreak such havok on our minds and bodies. Audre Lourde wrote her semi-fictional autobiography under the title of "Zami". Zami loosely translates to "Wemon working and living togeather". I feel thats as good an explination as any of my long winded attempts.
Eco-Anarchism and Primitivits pretty much explain themselves. As my experiance lies more in the economical, political, and realms of gender/sexuality rather then the ecological, Im going to leave these for someone else to tackle. Not everyone in these movements is part of the Earth Liberation Front. And not everyone condones their methods.
There are even those who claim to be anarcho-captalists. Dont buy it. Captalism creates hierarchy pretty much by definition. They are really just radical libertarians. Ayn Rand makes my head hurt.
Well, hopes this clears a few things up. Check out www.infoshop.org for more information.