I want to talk about anarchism, because it seems to be the default philosophy many power supervillains think is right for them. Most of what I want to say here will be what anarchism is not. But let's start with what it is.
Anarchy calls for the removal of the state as a source of governance. What is "the state" here? It's any community organized under a given government. The United States is a state in this sense, because of the Federal government. Individual American states could also be "states". Beyond that, there's as many modes of anarchy as there are Christian denominations, which figures - when you're not down with central authority, you're going to fragment.
Anarchy is not "do as you please". That's called "chaos". Anarchy is grassroots governance, not no governance. If you want an easy primer on the difference, go read "V For Vendetta" - not the movie, the original graphic novel. On top of that, V is a great supervillain template.
The Anarchic Avenue, an online blog, postulates that "true" anarchy is only possible in a post-scarcity society, and suggests that only Stage 3 superhumans can really participate in a meaningful anarchy. Whether that's true or not, there aren't enough Stage 3 and up people who have really tried, so we don't know. It would be an interesting experiment, though.
Anarchists, who reject the state by definition, have historically been clubbed worse than baby seals by any nearby cop, judge, or politician whose attention they draw. The case I first think of along these lines is the Haymarket Affair, back in 1886. The defendants - none of whom were particularly guilty of the crime in question - were variously described as "bloody brutes", "red ruffians", "dynamarchists", "bloody monsters", "cowards", "cutthroats", "thieves", "assassins", and "fiends". My kind of people. This trend has continued to the present day, when many supervillains will be labeled as "anarchists" regardless of their actual politics.
Should you be an anarchist? If you like long discussions that go nowhere but are highly educational, "pure" anarchism is your thing. If you enjoy the idea of social disruption, check out anarcho-syndicalism. Many villains are drawn to anarcho-capitalism because they think it means "a free market in which to buy and sell my shit legally".
Above all, if you think anarchism might be for you, educate yourself. That's really the first step in both understanding and practicing anarchy. One friend of mine says that if everyone understood anarchism well enough, everyone would feel like practicing it, and then it would spontaneously come into being as the default system of governance. In the spirit of her words, I encourage you to go out and read more for yourselves.