Anarchy is for Lovers
Anarchy is a tricky subject to discuss. As you can imagine, most people who identify with the concept of anarchy are hesitant to be the first jack-ass to assign any firm guidelines to the idea. So what we are left with is the vague waxing of 18th century philosophers, late 19th and early 20th century radical anti-government "direct action" anarchists, and modern day pissed off 14 year olds who are just flailing to be accepted. I expect they are all a little correct, and a little incorrect.
The core concept which most people agree on is to exist without the burden of external rule; all other discussions usually build from that foundation. The hope is to live a genuine existence, to develop ones own values and traditions based on how they see the world. Relationship anarchy, as with anarchy as a "political stance", should be approached as a guiding principle more than something to actually attain. Many anarchists dream to have a community in which the members (regardless of the size) reach a natural equilibrium; agreement by non-coercive consensus. They can theoretically live out their lives without putting much thought into it, yet from the outside looking in they seem to be acting out a well choreographed dance where the needs and abilities of each dancer supports and encourages the other without ever applying any pressure or correcting their natural rhythm.
In more direct terms, my view of relationship anarchy is much like the manifesto linked in my sig and in this thread. As long as I strive to let people be who they are, live by my own values, do no harm, and respect the fact that my fellows should be enjoyed - not controlled, I think I'm doing alright. I tirelessly question the values I follow and allow them to either stand or fall, according to their validity, all in an effort to be who I am and find a place of peace within the world.
In practice, I am still a new player in relating this way. I have very recently come into some difficulty and realized, again, that I have quite some growing to do before I will be able to smoothly and effortlessly relate the way I want to. Who knows if I'll ever get there, I've got quite a bit of baggage to unload, but we'll see.