(There are obvious problems with treating the Internet as a place, of course, and I blame sci-fi for a lot of them, going back to Neuromancer, and probably well before that. Sci-fi has stuck us with the gigantic lie that is "cyberspace", and convinced a lot of people that would otherwise know better that the Internet is a place, filled with things, which are separated by distance, and separated by [fire]walls. All of this is complete nonsense.)
What I'm talking about here is decentralized governance, maybe, until I find a better word for it. All governments and countries today are centralized in a really important way: centralized jurisdiction. The government has control, imperfect though it may be, over your presence in the country at any given time. They can force you to stay or to leave, and it's difficult to stay or leave without the government's tacit approval. There's a rough balance between the government's jurisdiction over you, and your ability to travel off the grid. This is enforced by the laws of physics, on some level: if we could teleport, for instance, or become invisible, the balance here would be very different.
Whenever there's a limitation imposed by the laws of physics, we can expect technology to take a crack at it. High speed transportation is changing the balance: with the advent of air travel, for example, you can pass through a country without ever being in it in any meaningful sense. This doesn't really change the balance in any meaningful way, though, because governments can simply step up control of airports, and pull the balance back in the other direction. Fundamentally, it's still the same situation.
Jurisdiction is important. It forms the basis for both laws enforced by governments, and services provided by governments. A military, for instance, protects a territory. It wouldn't make sense for countries to have militaries, unless there was a clear-cut equivalence between a government and the territory it owns. With an Internet-based government, though, you would lose that equivalence. When every citizen of a country can leave at will, simply by disconnecting, there are many services that it's impossible to provide.
You should be objecting at this point that this is all moot, since any Internet citizen would also be a citizen of whatever country they happened to be living in offline. While this is true now, it's not a necessary condition. We could imagine a region, with minimal (or without any) governance, designed specifically for people from various Internet nations to coexist. This could become arbitrarily ludicrous; imagine being a police officer in such a place, and not knowing whether or not any given person you saw was within your jurisdiction. Or, imagine trying to collect taxes from citizens that suddenly switch their allegiance for a few weeks every April.
Since I'm running short on time now, I'll just go ahead and assert that an Internet nation can only regulate what happens on its own servers and systems. This is not entirely useless, and a lot of services (especially identity-related services, which every government in the world is currently sucking at) could be provided this way. Even so, at this point we're talking about such a watered-down and neutered conception of citizenship that an Internet nation ceases to have any meaning at all.
Exclusive Internet citizenship is pretty much a bust. All is not lost, though. We could imagine a form of Internet dual-citizenship, where an online "virtual country" provides some additional services, and works with governments to provide them across national borders. (Actually, I really hope the phrase "virtual country" doesn't ever catch on. I'm starting to hate it already. >_>) This would represent a hybrid decentralization of government - doing what can be done in a decentralized way, but falling back to the existing central government for everything else.