The Punisher (real name Frank Castle) is perhaps one of the best examples of an anti-villain - created and owned by Marvel comics this vigilante is both a protagonist (with his own series and film franchise) and antagonist (regularly seen committing extremely violent crimes, although it is for what he views as a just cause).
Frank Castle was once an ex-Marine with a happy life and family, until one fateful and tragic day when he and his family accidentally stumbled upon a gang lynching in a park. His wife and children were gunned down, and it left him scarred for life. After that he swore to "punish" all criminals in any way possible, and became a vigilante.
The Punisher is a borderline sociopath who is obsessed with destroying criminals - he doesn't just solve crime, he punishes those who commit such acts: what makes The Punisher stand out from most anti-heroes is his tendency to utilize torture, execution and other illegal methods to get the job done and he is rightful feared and respected by those who know of him.
The Punisher has always blurred the distinction between "good" and "evil" but is as worthy of note as any other anti-villain / anti-hero in fiction (especially given his brutal nature).