The thing I like the most about blockchains is that they are unforgeable. Once something is published on the blockchain, it's there for the world to see, and there is no way anyone can go back on their word.
This has some amazing real-world applications, and we've all seen some of the cool things you can do with smart contracts. However, I believe this aspect of the blockchain has a much bigger potential than it is currently using, and imagine when smart contracts will be used by people who sell and buy real-life goods online. In this scenario a blockchain could be used to send the funds to the seller, but also make it so that these are locked in a smart contract until either the seller, or even the mail delivery service, opts to release it once the package it delivered.
In other words, the blockchain could potentially be a substitute for trust when doing a deal with someone, since you both post immutable transactions on the blockchain. And since it's transparent, anyone can go and look at the agreement and verify it.
And this does not just apply to trade between two people; organizations could use this to make public, unforgeable contracts, or manufactorers could use to to make unforgeable product supply data where each part of the process is stored on the blockchain and read by people who end up as users of the product. This latter example could help prevent things like slave or child labor, since people would be able to trust the information about the origin of the product, and no one wants to buy products from manufacturers who are known to use these types of labor.
So I think this part of the blockchain technology has a lot more potential than most people seem to think, and we will likely see more of this type of smart contracts in the future.
That said, there are also lots of other good things about the blockchain technology beside it being unforgeable, but I guess it will be up to other users to showcase these ;)