It's an idea as old as Xanadu, which predates the web by decades:
But see also:
- BitTorrent's Project Maelstrom
- GNUnet
- Tahoe-LAFS
- MaidSafe
- MojoNation, the technology that inspired BitTorrent
...just to name a few.
The problem with these systems is they don't provide a whole lot of compelling benefits over the regular web, and generally provide a worse user experience.
Solving the UX problem is the real hurdle to adoption.