Before now, most internet applications required there to be a central arbitrator to keep everyone coordinated. (Even so-called "decentralized" protocols would nonetheless nominate one of the peers to serve as a central coodinator. This is problematic when the central coordinator has an incentive to cheat and benefit themselves.) Going forward, we will see new versions of internet services that require no single entity to serve as a central arbitrator, but instead will use the network as a whole to keep things coordinated, even in an environment where some people have an incentive to cheat.

articles

• "Bitcoin solves a difficult computer-science problem, the distributed consensus problem -- how to get thousands of different computer systems to agree to a single dataset and timeline. That could have other applications, such as in Namecoin, which, says Garzik, 'uses Bitcoin technology to function as a decentralised domain-name system'."
• We believe the protocol will be leveraged beyond financial assets and fulfill the role of trusted intermediary in a variety of settings, including property, legal documents, escrow, sports betting, etc.
• "I agree with Andreessen that Bitcoin is the first practical, large-scale mechanism to deal with the problem of decentralizing trust—no parties need know each other nor trust each other for transactions to complete successfully, verifiably, and irrevocably. ... I also agree completely with Andreessen that Bitcoin can be used for an enormous number of non-currency related purposes in which permanent, irreversible proofs of transactions are required."

Bitcoin-variants that provide non-currency services

• Namecoin — DNS
• BitCloud — file storage
• Keyhotee — OpenID replacement

technical details

• for a great overview of how the Bitcoin protocol works, see this article [Reddit discussion]

Internal note:

• Here are some places to find new ones that appear: [1] [2]
• And the top-20 altcoins, which includes both currency-oriented and non-currency-oriented ones: [1] [2]