I think it would be pretty cool to have a simple, read-only API available for users' fiddles.
A real use case would be WordPress integration. For example, if the API would allow you to retrieve all the fiddles for a given user, you could create a plugin for the content editor that would allow you to quickly insert fiddles based on user. The returned data could then be used to create embedded fiddles.
So the purpose, as I see it, would be more about giving back the meta-data needed to craft an embedded fiddle, rather than providing the full data for the fiddle.
I'm thinking a result like so would be a good start:
In order to facilitate users with a large number of fiddles, perhaps the API could accept a start/limit combo for paging, and maybe accept an optional query argument as well for searching within a user's fiddle collection.