TorCoin. You proof of work is throughput on the network, a little for a bridge or middle node and a lot for an exit. Your Tor service is also a wallet and either the sender or the receiver has to spend to transmit data, and the spend is distributed among the nodes that handle it.

Somebody needs to invent something like this! Maybe they could start with a cryptocurrency with zero-knowledge proofs, and then add distributed public key messaging, then other features after that.