One possible use case: A notary for digital goods. Crypto currencies have a built-in incentive mechanism that keeps a ledger running and verifiable. This allows for a decentralized way to verify ownership of digital goods. More concrete, you could verify that you are the owner of a very rare sword you obtained in an online RPG. Even when the company goes out of business or stops the servers you could still prove that you own it. In other words, owners of valuable digital items might want their ownership to be stored on a public blockchain rather than a database by a private entity.