Distributed, decentralized, redundant, encrypted online file storage with the ability to share information with specific groups and individuals. From the user standpoint, a user would access their content primarily through client software that would ask for their id & password (or perform other authentication). The authentication process fetches a small file from the network and decrypts it using the user's identific…
Interesting idea, but I wonder how many copies of my data would need to be stored across the system to guarantee that at least one copy is available when I want it? Many people don't leave their personal computers switched on all the time, especially if they go away for a few days, then there are network outages, people deciding to leave the network, ...
Node A declares that it's quitting to Nodes B and C (or Nodes B and C are suddenly no longer able to poll Node A); Nodes B and C both check the chunks that they know Node A had, and see if there are enough redundant copies of those chunks in the network.
There's a lot of "and then magic happens!" in this idea, but I'm pretty sure it's do-able. The worst part of it by far is doing node searches on a completely decentralized structure.