A form of political ideology whose ideas are actually no more crazy than the ideas of other types of political ideologies; all have their flaws and benefits. Unfortunately, most people will never understand this because (1) they're too lazy and closed-minded to bother learning anything about the real meaning of the word "anarchist" and instead prefer to repeat the biased and generally inaccurate crap they were taught about it in their high school classes, and (2) within recent years, the word has sadly been stolen and had its meaning mutilated by stupid angst-filled teenagers who don't really understand the concept of anarchy any more than the average person, but love to call themselves anarchists because they think it sounds bad-ass. It's such a shame that the meaning of a word can be so thoroughly distorted by one clueless group of people who just happen to be really loud about it.
In 1850, an anarchist was not a twelve-year-old who wore an A inside a circle around their neck and went around yelling "Fuck the system!" and that's not what it is now either, despite what historically ignorant people say.