I've said this several times before on this site but will keep repeating it: there's exactly one use case where the blockchain is a superior (and, in fact, the only) solution: when you can't use contracts and the legal system to ensure trust between the parties. In other words, anything illegal. For any other conceivable use case, a database and a contract between parties are a superior solution. Edit: To clarify wha…
The blockchain is a self-sustaining PKI network. It eliminates MITM attacks and facilitates the use of PKI technology by making it trivial for nodes to read/write/verify information that is sent over the network. On the economic layer, the fact that it pays its own way eliminates the ability for network operators to create information-layer monopolies (i.e. App Store).
If you think about blockchain as a database, you'll be stuck thinking about the use cases that involve a database. If you think about blockchain as smart contracts, you'll be stuck comparing them to real world contracts. Start thinking of decentralized app stores (which cannot impose constraints on the revenue models of their hosted apps) or advertising networks which let users put advertisements on any webpage. There are tons of reasons to pay a small fee to send information across a secure and tamper-proof network.