The problem with creating a government-free internet for mass use is one of resources and determination as well as some technical difficulties in operating networks like this with large numbers of nodes. In rural areas the problems will be the longer stretches without connectivity as well as all the issues that come with routing packets around the world without network congestion if the number of nodes should get large or if something exciting were to happen.
On such a network the communications should be limited to the essentials, rich media is pretty much out of the question.
On another note, the frequency spectrum is highly regulated, powerful base stations operating as hubs could be shut down by triangulation and force and operating transmitters outside of the alloted frequency ranges is forbidden by law.
The only part of the electromagnetic spectrum that does not currently need any regulatory before equipment can be sold or operated is as far as I know > 10GHz, and even then there are strict limits on power. Other options are UWB: http://en.wikipedia.org/wiki/Ultra-wideband and optical links (for instance lasers).
In the United States the current frequency allocation chart looks like this:
http://en.wikipedia.org/wiki/File:United_States_Frequency_Al...
Setting up a 'government free' internet for a large number of users and without using existing infrastructure is a serious technical challenge, especially if you want to operate it without breaking the law.