Anti-Hero/Playing With

Basic Trope: A hero who doesn't have the qualities of a regular hero.
 * Straight: Billy is a vigilante who wants to make the world a better place by murdering criminals.
 * Exaggerated: Billy is a Byronic Hero.
 * Justified: Billy lives in a Crapsack World.
 * Inverted: Billy is an Anti-Villain.
 * Subverted: Billy appears to be killing crooks left and right, but it turns out he didn't have control of his actions at the time; when he's back to normal, he's The Cape (trope), through and through.
 * Double Subverted: Billy is revealed to have been Brainwashed and Crazy, and underneath that...he's just as brutal.
 * Parodied: Billy tries to bring about his own brand of harsh justice, but he lives in a Sugar Bowl society where there's hardly ever even any conflict -- Billy spends most of his time angsting that there's nothing to Angst about.
 * Deconstructed:
 * Billy is rapidly becoming just as brutal as, if not WORSE than, his villains, and when he's killed all of the real threats to society, he's still a dangerously unstable and violent individual.
 * Alternatively: Billy is arrested for killing a criminal because, as it turns out, murder is murder.
 * Reconstructed: Billy has a line he will not cross; the story runs on Black and Gray Morality or Gray and Grey Morality (with Billy as A Lighter Shade of Gray).
 * Zig Zagged: Billy has a very inconsistent attitude towards his crime-fighting; sometimes he's unwilling to kill anyone, sometimes he's killing left and right, and sometimes he's trying to be an Actual Pacifist. It's all Depending on the Writer.
 * Averted: All the heroes in the story actually act heroically.
 * Enforced:
 * "No one's interested in a flawless hero anymore, let's give this guy loads of issues and have him be all morally ambiguous!"
 * Alternatively: The author is trying to prove some point about the nature of heroism, or else is deconstructing The Hero or The Cape (trope), which requires Billy do some questionable things in the name of justice.
 * Invoked: Billy is a sadist, so he decides to start taking it out on the people who society says deserve it, lowering the crime rate as he does so and leaving the town happier for it.
 * Defied: Billy feels himself slipping into antiherodom, and works hard to maintain his moral code.
 * Discussed: "Billy's not exactly a nice guy, but he's on the side of good. No, really."
 * Plotted A Very Good Waste: Billy's morally questionable actions make him a much more interesting character and are used to analyze what "the qualities of a hero" truly are, and what makes someone heroic.

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