Traditionally stories are categorized into types based on their chief characters' position in the narrative. These are the types that I know of.
High Mimetic: In which the central characters are above our own level of power, action, excitement and authority. This is often over dramatic. Check out Odysseus.
Low Mimetic: The characters are basically just like you or I, going about their business in the everyday world. Jane Eyre would be a good example.
Irony: The characters are inferior to us. The story may be about social misfits and criminals. A Clockwork Orange or A Confederacy of Dunces would be good examples of this.
Myth: A lot like high mimetic, but the people tend to be more than human, and the events take place in a world apart from ours in some sense (the past, or in magical worlds). Achilles is probably a good example of this.
Romance: A confusing one, this. The chief characters live in a world of wonders. David Quinn thinks that the characters should be nobility or superior beings. Other sources don't specify that, but aren't very clear on what they are specifying. I'd like to put Alice's Adventures in Wonderland in this category, even if she isn't all that noble.