Anarchism has gotten a bad rap, and it's really no wonder why. It has been systematically demonized by the press and public officials, equated with terrorism, put down as the self-indulgent fantasies of adolescent boys, or simply labeled “impractical.” I have no doubt that there are some anarchists who are only in it so they can blow shit up, and there is a nebulous conception in many anarchists minds about what it would look like in practice. There is no unifying principle, nobody dictating what to do, and that makes it difficult as well as opening the door to a lot of people with their own agenda. But the majority of anarchists that I've met are kind thoughtful people, who have spent a lot of time working through the ambiguities and distortions in order to live better lives.
There are a lot of misconceptions surrounding anarchism, both outside of and within the community. It is not an ideology, but rather a lack of ideology or better yet an anti-ideology which says that any centralized, abstract, bureaucratic power structure is inherently oppressive and should be resisted by any means possible. The Marxists got it wrong by handing power over to the state, and the capitalists got it wrong by not reigning in the corporations.
Anarchism doesn't imply a lack of social structure, it seeks a reorganization of society to limit the reach of power. The ideal system is one which disperses power keeping it as localized and small scale as possible. In the words of Edward Abbey “Anarchy is democracy taken seriously.” It is not a utopian vision; there will always be problems to overcome and challenges to be met, but it is the most appealing social structure to our collective nature.
The question of practicality is more difficult. For most of our existence humans have lived without these complex power structures, in fact, they didn't develop until well after the adoption of agriculture and settled societies about ten thousand years ago. However, most modern attempts at anarchism, such as the Israeli Kibbutzim, the CNT of the Spanish Revolution, and a few experiments that arose in the chaos of the French Revolution, have been small scale and short lived. With modern population levels and international politics being what they are, it's doubtful that any anarchist community would last long. For now, we must be content to carve out a small space within modern society to live and work together in the spirit of mutual aid.