"Sin City" is self-consciously operating within the Film Noir tradition of the 1940's and 1950's; these films were often based on published novels and stories written in the first person, where the protagonist narrates the action. This technique was often carried over from the stories to the film versions.
The predominantly black-and-white cinematography is an homage both to Miller's original graphic novel and to the great Noir films of the classic era. Personally, I enjoyed 'Sin City' a helluva lot, both the books and the film, since I'm a pushover for the whole Noir thing!
Try 1947's "Out of the Past", a classic noir starring Robert Mitchum and Jane Greer, where the protagonist's shady past is catching up with him, despite his efforts to go straight. You'll find many of the classic tropes and tags of the genre right here - it's a good intro if you're interested in following up on these films.
"I, The Jury" (1953) is another, far more brutal film, where the protagonist, private eye Mike Hammer, seeks revenge for the murder of a war buddy and wades through an ever-increasing number of corpses to get to the truth. Hammer resembles Sin City's Marv, in his single-minded determination to get revenge, and his impatience with 'conventional' processes. The use of extreme physical violence to achieve their ends makes both Marv and Mike Hammer similar uncontrollable outsider figures.
The original Mike Hammer stories (by Mickey Spillane) are written in the first person, and can be characterised by their angry and misogynistic tone; by today's standards, Hammer is an unrepentant racist and sexist, so much of the language would now be considered extremely offensive. Hollywood production codes of the time meant that much of this could not be transferred to the film versions, which are much tamer by comparison.
See also 'The Big Sleep' (1946) and 1940's 'Stranger on the Third Floor', both iconic examples.