Once, before film, before printing, before even writing, all stories were spread by word of mouth alone. If you wanted a story, you had to get some old fart to actually sit down at a fire and tell you, and you usually had to put up with a lot of tangential rambling, too. Most of the oldest stories have their roots in this ancient storytelling medium.
Oral storytelling has distinctive features, shaping the tropes it uses. Speech is not nearly as fast as reading, so an evening's worth of story is shorter. It is not possible to page back through an oral story to make sure it's internally consistent, and the story itself needs the kind of repetitive features that aid memorization. Even with memorization, stories usually change over long periods as the details of the original telling are altered by different storytellers, by innovation, to suit various audiences and circumstances, and by cultural and linguistic changes.
Nowadays, you kids with your new-fangled "writing" and "movies" tend to think of Oral Tradition as a medium of the past. But even in the most literate and high-tech cultures, stories, beliefs, ideas, and jokes continue to circulate orally as long as people continue talking to each other face-to-face or via telephone. Online social networking will have to become even more omnipresent before Oral Tradition really dies as a medium.
The genres most often associated with Oral Tradition are Myth, Legend, and Folklore (folktales, fairy tales, folk ballads, folk songs, etc.), or just Mythology. These genres are not just oral — many mythological works have passed into or originated from other media such as writing and theatre. But these genres originated with oral storytelling, and are frequently referred to collectively as "oral tradition."
An oral work, once written down, isn't Oral Tradition anymore. The oral versions can still wander around, and often do. But the written version is now Literature, and will change independently from the oral versions. This is an important distinction for this wiki, because the two media are subject to different types of adaptation, circulate by different channels, and often employ different tropes. It also comes up in the style of the wording, for example the repetition in oral works vs. the richer description, more detailed narration, and illustration that usually only shows up in writing. Once a work is written, it's much easier for the author to look back over the whole thing, removing contradictions and inconsistencies, before presenting it to an audience. This is not to say that tropes from the oral tradition do not show up in written media at all: usually, there is a transition period when a story moves from oral to written form. This can be seen best in early literature, which still rely on repetition, formulaic storytelling, and rhyme schemes in some form or another (consider that poetry used to be the MAIN form of storytelling because of this). Nor to say that oral tradition is independent of literary versions: the Brothers Grimm correctly deduced that some of the oral tales they collected were in fact derived from Charles Perrault's literary tales, and a Japanese folklorist established that the publication of their works produced noticeable changes in the fairy tales told in Japan; the fairy tale Beauty and the Beast, originating as a literary tale using fairy tale motifs, has reappeared in many variants in oral tales; and folklorists talking with storytellers are often told of their actively seeking out literary sources to increase their repertoires of stories and motifs.
Since oral works by definition aren't written down, it's almost impossible to trope them. The works troped on This Very Wiki, even those that originated in Oral Tradition, are almost all adaptations in other media.
See also Language Tropes.