6 degrees, though. The network of connecting one person to any other person on the earth is usually quite small.
Hmm.. here's a silly idea.
A peer to peer network, let's go with a cool web-2.0-ey name like Chaffr, that assigns you a GUID and establishes a stream of truly random (or pseudorandom) data which is propagated out via a P2P system kinda the same way Tor nodes communicate with each other.
This stream of noise is generated and runs 24x7. Might require a hardware dongle of some kind to keep the entropy pool full enough.
This data is random for the most part, but if you have the GUID of another user, you can send them messages which will be encoded into the stream and received by the other person either immediately, at a set time, or at a random time inside a given window.
Garbage, uncompressable, unusable data for the snoops (and the nature of the system as explained in the Snowden leaks will require them to store every useless byte), an anonymous, decentralized communication network for everyone else.