While encrypted currencies have been gaining attention as of late, other uses of a distributed, encrypted network are available. Bitcoin and many of its alternatives use a file called a blockchain as a register of transactions and network activity.
Now, the main issue is the size of the file can increase greatly as the number of coins/activity/transactions does. If Moore's Law tapers off and no rare earth substitutes are found, much electronic technology could stagnate (and with it, a potential hard limit for cryptocurrencies). However, even if this is the case, smaller networks could be spun off to act as nodes or regional/national alternatives.
One potential idea is voting and political activity. Imagine if instead of just currency, a "proposal" file could be sent out to multiple addresses on the network, and then positive or negative (or "modify") votes be tallied up. The success/failure of a proposal (as well as versions of a proposal) could be recorded in the network, available to all. There is the risk of vote manipulation (as with most democratic systems), but another variation is delegated voting, similar to how the Pirate Parties operate. Any designated delegate would have their record open and able to be recalled at any time. Another idea is that each 'block' of addresses could be further subdivided (like Bitcoins can) to assist with smaller scale decision making. Also, any "voter" could propose a law or changes to it, as with Swiss semi-direct democracy. Perhaps even a "judicial" branch or clade could argue over reforms, much like under the wiki system. I also imagine setting up a "Bill of Rights" or user terms could act as the "social contract." Of course, it need not be grand, as it might be scaled for university clubs, sports teams, or corporations as well.
I imagine such a system could exist independent of an existing polity. It could also reinforce democratic and desirable representative aspects and limit non-democratic aspects. There are two primary ways (or a combination of them). One is that the digital democracy acts on a regional/local level, and another is that it's distributed across the world in the manner of a distributed republic. In addition, it could be combined with cryptocurrencies and crowdfunding to achieve its goals (such as building non-profit groups to run 'utilities,' funding legal/political campaigns within the existing system, etc.). Whether the local government is a dictatorship, representative democracy, communist state, or monarchy, the members of such a network could be harder to locate, and would be able to manage funds/resources independent of existing polities (or offer alternatives to them). Eventually, users of such a tool may take or be elected into office themselves, moving it from an alternative system into the new mainstream. Plenty of ideas start off seeming crazy, but become the ruling law as people age and new generations replace them.