Well, for a bank it can be super duper useful because it's "incorruptible digital ledger of economic transactions" (the very definition of a blockchain). So if you're transferring money from one bank to another it makes it all but impossible to mess with that transaction in flight (man in the middle attacks, timing attacks, replay attacks, etc).

Another example would be trades: Most people think of trades as buying stocks and bonds in an open market but there's a lot of private/internal-to-an-organization markets too. The blockchain is an excellent way to facilitate such transactions.

Being in banking (where we're trying to take advantage of blockchain transactions) the objections from management so far have been surrounding the inability to "undo" a transaction. Even though you can just make the same transaction in reverse afterwards the price of whatever it was that you're trading could've changed resulting in some troublesome circumstances.

For it to work you have to negotiate contracts ahead of time to ensure that all parties participating understand the ramifications of such a system. Since the blockchain is new technology it will be difficult to get 3rd parties to sign of on such things.