If Internet censorship continues to the point of all Internet usage is monitored what will happen?

If the gov't starts enforcing copyright protection on a HEAVY person to person basis, will there be a rogue group of hackers or people just keeping up servers so people can surf unmonitored (what I think the movie version would be like?) Or will people just give up and not do anything illegal online whatsoever? I hope for the first one. What do you think?