Digital Pokemón Cards.
Basically the ability to create digital collectors items.
E-books that could gain value.
You could sell ebooks at a premium and allow people to re-sell them. Because the history of their ownership is recorded you could even see them gaining value if they had been owned by a celebrity.
Private but public healthcare records.
For research and usage. Store the health-records publicly as personas but allow individuals people to link it with their identity. This would help with research in completely new ways.
Voting made public but anonymous
Make it impossible to fake voting results by making the results available for everyone.
Using the protocol to create automated consensus models.
Companies without owners
Build a company with a political purpose without any owner.