Focusing on the age:
* Ancient tale: Emphasizes the story's age and often implies it has a mythical or legendary quality.
* Time-worn story: Highlights the story's age and its potential for being passed down through generations.
* Age-old narrative: Similar to "time-worn story," suggesting a long history.
* Centuries-old legend: Emphasizes the story's age and its possible fictional or exaggerated elements.
Focusing on the repeated telling:
* Folklore: Refers to a body of stories and traditions passed down orally.
* Legend: A story that has been passed down through generations and often has a historical or mythical basis.
* Myth: A traditional story, often involving supernatural beings, that explains a natural phenomenon or cultural belief.
* Oral tradition: The passing down of stories and knowledge through spoken word.
Focusing on the impact:
* Enduring story: Highlights the story's lasting impact and relevance.
* Timeless tale: Suggests a story that remains relevant across generations and cultures.
* Classic tale: A story that has become a recognized and admired example of its genre.
Ultimately, the best word depends on the specific context and what you want to emphasize about the story.