I would conjecture that VPNs and similar solutions for secure communications might be authorized to be run only by licensed operators (and that part of the licencing requirements would include a functional back-door for what's known as lawful intercept.)

I also suspect that one may need to establish identity via bio-metrics or some other fool-proof method prior to being able to access the internet at all.  It'll be sold as big brother's helpfulness in overcoming the problems of identity theft and stopping those bad bad terrorists and the massive amounts of kiddie porn hiding out in the ether.  And I figure that it will be massively popular with the sheeple.

I'm not saying that such things are eminent or certain, but it does seem to me very possible that attempts in those directions will be made.  In conjunction with draconian penalties they probably could be fairly effective.  Certainly enough so to put a damper on so-called 'intellectual property theft' which is driving corp/gov crazy and something like Bitcoin in it's current implementation.