I don't know if the governments of the world can do anything about this, but they're going to want to try. If they don't know how much money I have, then they can't know how much I should pay in taxes.
I think we're already starting to see this play out with Anonymous. They're trying to crack down, but having difficulty.
I'm interested in seeing how crowdfunding might work for projects traditionally funded by taxation. One example: http://neighbor.ly