Many types of stories from the oral tradition fall under the umbrella of folklore.
Myths are origin tales that often explain natural phenomena, emotions, or social occurrences.
Legends are tales that have allegedly occurred and feature heroes and their triumphs.
Folktales and fairy tales reveal human behaviors, attitudes, or foibles; occasionally serve as warnings, and often include magic
Fables often use animals as vehicles for teaching morality.
Parables are meant to educate, often religious in nature.
Drolls are Japanese in origin; they are usually funny "introductory tales" that are told before a longer story
Tall Tales are hyperbolic tales, occasionally sprinkled with truth
Urban Legends are modern tall tales, cautionary in nature
Most folktales and fairy tales come from the oral tradition, meaning their origins are indeterminate - there is no known author. Because of this, many folktales are shelved in the social sciences section of libraries; they are an inextricable part of a culture or society.
The specific call number of most folktales and fairy tales is 398.2. It is here that you will find many familiar stories ("Cinderella", "Little Red Riding Hood") as well as lesser known folktales ("Sense Pass King", a folktale from Cameroon) and cultural variations ("Sugar Cane", a Caribbean version of "Rapunzel").
It is also common for some tales to bleed into 398.3 and 398.4.
I personally recommend browsing these sections - you never know what treat you might come across!
Some folktales and fairy tales do not come from the oral tradition. Rather, they are the product of a specific author. For example, Carl Sandberg wrote a number of American folktales called "Rootabaga Stories".
Because these stories have a traceable origin - that is, their provenance is definite - they are shelved in the 800 section of libraries. It is in this section that you will find stories by Hans Christian Anderson, Oscar Wilde, Jane Yolen, Rudyard Kipling, and others. The specific call number varies by both geographic region and time period.