There is some argument about terminology, whether the notion of blockchain includes the peer-to-peer distribution and consensus mechanism (eg proof-of-work) or not. (In my view, it shouldn't.)

Git uses a somewhat extended version of a blockchain (a directed acyclic graph instead of just a linked list).

I think it's a cool technology, and has many applications where you want an immutable sequence of records. But it's not a panacea, and the current hype is overblown.

Close to cryptocurrency, but reward points seem like a good use case. That is, something very seamless to move rewards around whether they were earned for a hotel, airline, credit card, etc. Points.com takes a pretty big cut for that (centralized) service today.

Money transfer as well, maybe. I don't know the space well, but it seems like MoneyGram, Western Union, and similar charge a high premium for their services in some cases.

Almost anything that needs validation/integrity.

Luxury handbags? Check the blockchain to confirm it is real.

Need goods transported at a consistent temperature? The blockchain can validate that your shipment did in fact remain (or not) at a certain temperature.

Want to buy a scalped ticket? Scan the QR code and confirm the ticket is usable.

Here in Moscow it is now used in Active Citizen program for polling. + Anyone can install a piece of software and monitor polls in real time.

https://en.wikipedia.org/wiki/Blockchain#Applications lists many use cases: land registry, online voting, crowd sales, supply chain management.

Use of clearing for financial markets. You'll be able to verify that party A has the instrument and party B has the currency without needing to go through a separate company.

Ethereum is banking on smart contracts. Contracts that trigger when the conditions are fulfilled and automatically transfer the money.

Bitmessage. It's email and mailing lists alternative based on block chain

proof of digital asset ownership.