Probably a web server which stores data in a distributed (and fault tolerant) way in all these clients. There will be no central point of failure. This will be really worthy of being called "cloud" as opposed to a bunch of servers put together in a farm.

In addition to the advantage of being fault tolerant, a system like this will be able to balance the load in such a way that the website never goes down in case of a traffic surge.

Another benefit (or not, depending on how you see it) will be that a website hosted in a torrent cloud will be difficult to take down by anyone.

Some interesting ideas ....

- Make it easy for people to get TED talks via. BitTorrent with recommendations

- Share your torrents with friends in a Blippy style feed

- Make something feel good, like a map with the general locations of all the peers you're connected to.

Integrated search of popular torrent websites.