CryptoKitties has done a great job of demonstrating what blockchains can be used for beyond just simple financial transactions.
It’s basically a game for buying, selling, and breeding digital cats. Each cat has a unique appearance that is defined by its genes, and when you breed 2 cats together, their genes combine in a unique way to produce an offspring, which you can then breed or sell.
Source code: https://ethfiddle.com/09YbyJRfiI