While not being an
anarchist myself (I went through that
phase during
junior high school and so get to
mock fellow college students wearing
anarchy patches bought with their parents' money), I've read enough to know that
anarchism does not reject the idea of
organizations,
tim_three's writeup aside. (Strangely enough, the one source of information that stuck in my head the best was a
didactic college comic strip with a anarchist protagonist)
The idea behind anarchy is the lack of non-consensual organizations and institutions. If you do not wish to follow the laws, rules or morals of an institution, an anarchist feels one has the right to ignore them. As one can imagine, this hardly makes the police, the government or the authoritarian priests of organized religion happy, since according to the idea of Deep Anarchy such beliefs challenge their very existence. This doesn't mean that no organizations should exist. Actually, most serious and intelligent anarchists work hard on building local area-based organizations as a way to decentralize social control and so allow the community to avoid interference from non-consensual institutions. Of course, the majority of anarchists are either alienated adolescents or "I'm more politically aware than you" activists with the resulting alpha male primate power struggle typical of groups that claim to be completely equal, but there's a few clued individuals out there. They're simply more idealistic than most people, who think some amount of non-consensual order is necessary.
My conclusion of that fact, incidentally, is why I gave up on anarchy and became a libertarian several years later. But I still feel the ideal in my heart, if not my head.