The anti-hero is not simply a protagonist who does bad things. That definition collapses too many distinct types into a single category and fails to account for what the anti-hero is actually for. What distinguishes the anti-hero from the villain protagonist is orientation: the anti-hero is still the reader's primary identification point, still the narrative center of gravity, but they expose a gap between the moral framework the story inhabits and the behavior that framework was supposed to produce. The best anti-hero novels use that gap to say something about the inadequacy of conventional heroism, not simply to celebrate transgression.
The Stranger by Albert Camus is the foundational modern anti-hero novel. Meursault doesn't experience guilt, grief, or social obligation in the way that society requires him to, and the novel's argument is that his absence of conventional feeling is, in certain lights, more honest than the performances of those who judge him. Camus is not endorsing Meursault's shooting of the Arab — the novel doesn't offer that kind of endorsement — but he is asking whether the social structures that condemn Meursault for the wrong reasons (his indifference at his mother's funeral rather than the murder itself) have the moral authority they claim. Meursault's anti-heroism is philosophical before it is behavioral.
Blood Meridian by Cormac McCarthy has no conventional anti-hero — the Kid, the nearest thing to a protagonist, is defined more by what he refuses to participate in than by anything he does. But Judge Holden is the most complete anti-heroic figure in American fiction: he is a philosopher of violence who articulates the logic of his own position with terrifying clarity. "Whatever in creation exists without my knowledge exists without my consent," he says, and then acts on that premise entirely. McCarthy gives the Judge the most powerful voice in the novel and refuses to undercut his logic from within the narrative. The reader must hold the Judge's coherence and his horror simultaneously, without the novel resolving that tension for them.
Invisible Man by Ralph Ellison is an anti-hero novel about a protagonist who learns, across the course of a long education in disillusionment, that every system he has invested in — the black college, the Brotherhood, the ideal of self-improvement — has been using him rather than serving him. His anti-heroism is not moral failure but political awakening: he becomes the protagonist of his own life by refusing the definitions that others have imposed on what his life is supposed to mean. Ellison wrote one of the great American novels about identity precisely by making his narrator resistant to the category of hero that the novel's cultural context demanded.
Dostoevsky's Underground Man — the narrator of Notes from Underground (1864) — is perhaps the purest anti-hero in the literary tradition. He is petty, resentful, self-defeating, and aware of all of it. His awareness does not improve him; it makes him worse, because he can see what he should do and cannot make himself do it. Dostoevsky was writing against the idealistic rationalism of his contemporaries — the argument that human beings, given sufficient knowledge of their self-interest, would choose the good. The Underground Man is a systematic refutation of that argument: a man who knows what's good for him and refuses it out of spite, who prefers his own humiliation to the condescension of being improved by a rational program.
The anti-hero is a persistent type in literary fiction because it solves a recurring problem: how to write truthfully about moral failure without either condemning it from above (which produces didacticism) or celebrating it (which produces nihilism). The anti-hero lives in the space between those positions — a person whose inadequacy is fully shown, whose perspective is genuinely inhabited, and whose failure illuminates something about the system they fail within. The best anti-hero novels don't resolve that tension; they hold it open, which is harder and more honest than either of the alternatives.