This depends on us. If we use bitcoins, or other alternative currencies, without caring about governments, they cannot do much.

There is already the Tor network, and alternative banking may be done using Tor hidden services.

What is necessary for this to work on a large scale in a reputational network, with volitional arbitrage. See http://ilja-schmelzer.de/network for the concepts which have to be realized yet. But once such a system works, governments cannot do much to destroy it. To forbid it is simply not sufficient.