Source Code Hosting (GitHub)
Of all the things that should be composed entirely of distributed, open source software, Github is at the top of that list.
It's largely a combination of two other use cases listed here: sort of a mashup of Dropbox and social networking features.
Git itself is flexible enough that a bridge like git-svn can be written to allow Edsu to be the storage for git repos. Both git and Edsu are based on content-addressed storage, so it's likely that there won't be any terrible impedance mismatches, and in the worst case Edsu can emulate a simple filestore, which git is already compatible with.
It does highlight one of the biggest challenges inherent in any distributed system, Edsu included: discoverability and search. Even though devs can host their own repos, someone needs to index all of them, and also provide a place to register their existance.
This "re-centralizes" things, with all of its advantages (convienience, efficiency) and disadvantages (the need for moderation and coordination, and the tendancy towards monopoly). The one nice thing that a federation of Edsu git repos would have is that at least the indexing would be lightweight - the content (repos, comments, etc.) live on devs Edsu servers, the only thing that would need storage is the index itself.
So in the scenario of "GitA" becoming a central place to search for open source projects and then becoming evil, a GitB could come along and cheaply provide an alternate index. Everything else - the repos, discussions, bug reports, etc. would remain just as they were and equally accessable to both GitA and GitB users.
Of the use cases presented here, this one is probably the hardest, but also the most important.
That's it for use cases, thanks for reading! From here, if you haven't already, you'll probably want to dig deeper into Edsu at the In Depth section.