Which of these words best describes a story that has become widely known over time?

The word "legendary" is the most fitting choice to describe a story that has become widely known over time. A legendary story often carries a sense of tradition and has been passed down through generations, gaining prominence and recognition in popular culture. These stories typically include elements of heroism, adventure, or myth, making them memorable and impactful in the collective consciousness.

In contrast, contemporary would refer to something current or modern, which does not imply a long-standing reputation. Narrative simply describes any account of connected events, without the implication of widespread recognition. Lastly, obscure indicates something that is not well-known or is difficult to understand, which stands opposite to the idea of a widely known story. Thus, "legendary" captures the essence of a story that has achieved a notable status over time.