There are projects like gridcoin, uscore dot net, that use mining to compute scientific research. It is considering using a Proof Of Research approach.
It would be game changing if blockchain mining efforts could be applied like this to other uses as well, like someone needing huge datasets analyzed and formatted into a presentable state on an ad-hoc basis, sort of like AWS Athena.
Just found out about Filecoin which is an interesting concept, you "mine" by storing and serving files people save to the network.
Stuff like this is a much more interesting use of cryptocurrency and blockchain technology in my opinion, instead of burning electricity for PoW you can do meaningful work while collecting a reward.