Golem has the potential to solve the Cloud Trustworthiness problem, and it's an interesting problem one with huge upside if it we ever get there. How do we verify that the the code we're running (e.g. the VPN we have set up on a VPS in the cloud, or the web server we're connecting to) is actually running the code it says it's running?

Ethereum can do that (because it's just one giant computer running the same code and verifying it's state after every functional call), it's just really, really slow and insanely expensive. Perhaps they'll figure this out, if they do, it will be awesome.