Honestly, cryptocurrency is an example. Some cryptocurrencies don’t have mining and so aren’t all that bad, and there is a use case for it, even if most of what we see today is hype.

Another example might be something like a way of proving something happened before a certain time. Like how people can send themselves sealed letters in the mail, and claim that the postmark proves that it was sealed before that date. If you put cryptographic signatures only into a public blockchain, that could be used as evidence that the document existed at that time.