What happens when stories leave the page?

We’re used to reading stories start to finish with the path dictated by the sequence of the pages. But with digital technology there is no need to impose such a rigid structure on how an audience digests a narrative. We’re already accustomed to browsing data on the internet without regard to any direction but our own, and a video game certainly increases the audiences involvement in determining the course of a narrative. But we haven’t yet seen many writers embrace the new possibilities. Or at least if they are I’m missing it.

What might narratives free’d from the structure of page and binding become? How would it change the roles and experiences or author and audience? What narratives (regardless of their media) already do this?