Using the Napster model, users searching for a particular MP3 file log on to the Napster server using the Internet to conduct a search. Napster then searches for the files through the PCs of the other users connected to Napster at that time. When it locates the file, Napster redirects the requesting computer to the responding computer and the transfer is performed between the peers. User PCs download software from the Napster site to help connect to the service and to manage the requests for downloads and outgoing connections. Napster has solved a seemingly complex problem with both elegance and style.
Software distribution comes to mind, and seems like a good place to start.
This approach to distribution would require only a fraction of the time it takes to otherwise distribute the software or software patches. Rather than maintaining specific auction item details by updating the Ebay or Amazon Auctions databases, why not use those services only for the meta-data on the items, but keep item details locally and under user control. Under this approach, updates on items offered for sale would be instantaneous, data integrity would improve, and the overall auction shopping and buying experiences can be vastly improved. Another sticky problem that P2P might help to solve is catalog data for both B2B and B2C sites. Security notwithstanding, using locally stored copies of catalog information that serves as a single source or single point of information would greatly improve information flows throughout the supply chain.