Train some mad, distributed neural nets or some shit.
Gather image/art data and train a net to determine beauty.
Solve all possible sudokus so the world can finally be free of that junk.
Make cloud-driven instant facial recognition (via social media images) a thing.
Build a huge pi-as-a-service, and use it with pifs (https://github.com/philipl/pifs)
Bonus points: worlds biggest lolcat host.