Anti-hero
An anti-hero is a literary figure that, while they are the protagonist of a story, they're not essentially heroic in that they do not conform to expectations of heroic figures.
--Attributes-- A classical hallmark of a hero may be their predilection toward brave acts, or bravery in general. A famous brave hero in Norse mythology is Beowulf. Beowulf slew the monster Grendal and saved many villagers. This interpretation of a hero is common and fits with most readers' expectations. An anti-hero, by contrast, may be a coward. For example, in the popular children's television program Scooby Doo, Scooby and Shaggy are cowards--seemingly afraid of their own shadows--yet capable of solving mysteries. Their cowardice is antithetical to most readers, yet readers will identify with them for other reasons (their humanity, possibly.) Without Scooby and Shaggy, mysteries on the program could not be solved and thus their position as co-protagonists is secured.
Anti-heroes will often cause a reader or audience member to feel a conflict about supporting the protagonist's goals. Many of actor Clint Eastwood's early roles in Sergio Leone's films, as the "character with no name" were focussed on the narrative of an anti-hero. Eastwood's character would sometimes ignore an opportunity to help someone i need if he didn't feel like it, or act in some way that called attention to his character's moral ambiguity.
A well-known example of an anti-hero is the character V from V for Vendetta.
See Also
The traditional protagonist, the hero