-Voting and the democratic process.
-Tracking guns.
-Logistics and supply chain management (tracking of goods)
-Other distribution (e.g. who the rightful owners of an e-book are)
-Betting through the use of oracles - this can be done P2P.

You have to think of the blockchain in this instance like an easy way of verifying ownership and events that happen.  That's what results in the best use cases.