Notes from the Underground
The Underground Man
Many have called the Underground Man one of the most influential "anti-heroes" in literature (here is one example). As a protagonist, he has all the qualities that a protagonist shouldn't have. He's weak, passive, and unattractive. Since Notes is considered a forerunner to existentialist literature, this fits the bill; anti-heroes were a key part of existential literature (think Meursault The Stranger by Camus, or anything written by Samuel Beckett).