Things that come to mind are Namecoin, I2P, IPFS, and other tech on the pipeline that can bring the internet closer to it's original ideal of distributivity, each person responsible for their content, etc.
Those are also free software ideals: while great strides have been made in open sourcing user-side software, (mainstream android, Linux on servers, etc), the internet just hides a massive closed system: before you could at least inspect how things work through reverse engineering, but querying web servers is literally a black box model. The problem that not everyone wants to run their own server or even deal with renting out can largely vanish from certain applications. We've started with the easiest ones, which were file sharing (reputation-free), then Bitcoin, with more basic web tasks incoming.
It's important to keep in mind most of those are fit for low-efficiency. Unless we have a breakthrough with Fully Homomorphic encryption, the bulk of computing itself will be centralized (or you will have to accept a mix of high cost or unreliability).
I didn't cover the case of smart contracts, but it's essentially the same thing.
Ok, and what concrete, real examples does not benefit from that?
For example, this could be a rendering problem: you provide the models, a distributed system computes it (for a cost). This system cannot be private, efficient and reliable. It can be private and reliable, but hugely inefficient, or efficient but non-private and non-reliable. With a non-distributed system (i.e. Google compute, Amazon cloud, etc) you get pretty much all 3 of them, with a slight caveat that privacy is guaranteed circumstantially/legally instead of mathematically. But it's extremely safe to assume you'll be fine.
You want to run and real time multi-user application.
For example, and MMORPG. This one is a fun challenge for sure, but it's a complete nightmare to develop, and again needs sacrifices. In this case you probably can't achieve speed, security, and large number of players simultaneously. Every decision (like "what did this monster drop?") needs to be done through some large scale consensus to guarantee security, which kills latency completely. If you're extremely lax with security and consistency, then you can probably make it work, but accepting users might cheat, possibly game-breakingly. Or you could achieve it all with a handful of players, and reasonable efficiency[1], but your scope will inevitably be limited. I believe Ubisoft's ForHonor[2] uses P2P gameplay, but I'm not sure how safe their system is. Also I'm sure stats and most persistent data is stored centrally.
[1] See Mental poker:
https://en.wikipedia.org/wiki/Mental_poker
[2] Some reddit discussion from quick googling:
https://www.reddit.com/r/forhonor/comments/5u8jlh/why_forhon...
Note that the players largely loathe this system.
Lots of folks are working on different, less wasteful ways of making blockchains more resistant to attack - the most well-known of the alternatives being proof-of-stake which is essentially a betting scheme. It's a fascinating area of computing if you go beyond the hype over the BTC price.
Unless you're buying/selling or paying for things with cryptocurrencies, then, no, you probably aren't encountering any blockchain tech right now.