Q:

How can citizens prevent government-led Internet blackouts?

The United Nations now considers Internet access a basic human right. [PDF]
Despite the questionable effectiveness of Internet blackouts in silencing a populace and preventing uprisings1, it's worrying that governments can flick a kill switch, as they did in Egypt on 27 January 2011. To that end...
Can concerned citizens take any security measures to prevent government-led Internet blackouts, and if not, what methods can they use to establish secure Web access when their country's ISPs go down?
1: Conan O'Brien famously said that, if the Egyptian government wanted people to stay at home and do nothing, they should turn the Internet back on. [source: YouTube]

A:

Preventing government-led Internet blackouts is highly unlikely, since governments have very close ties to the telecom industry for a reason. 
By the time Effects-Based Operations on that scale are in play, the likely outcome of a conflict is already decided. Voice communication would be of much more value, and that's a completely different question in my opinion.
To answer your question though, while satellite internet access as Thomas Pornin points out is possible, using dail-up connections over a land-lines or mobile phones to international access points that in turn connects to a encrypted channel would be the most likely solution. International dial-up numbers will only work with international calling service that's working and methods to pass the audio signal to the access point via the phone. Here's an example of instruction on how to connect, and a list of dail-up ISPs access points.
Ham radio users also might be of use, for example, Telecomix, a group of Europe-based Internet activists, were aiding Egyptian protesters for days.  They were trying to establish contact by amateur radio or shortwave, and then forward the audio signals from modems in Egypt to the Internet. 

A:

Access to water is essential to human survival but that does not mean the government does not have a vital role.  Their critical infrastructure role can be done with respect for citizens' rights or not.  In a democracy the answer for citizens lies not in security solutions but rather in the ballot box.
---updated with expansion below---
The Internet is a government creation given to the citizens via a grant to industry.  There are many controls that any government can exert over the Internet to curb or stop access completely.  A change to DNS, a directive to ISPs, or simply tracking and punishing behaviors through technical or social means (neighbor watch of the coffee bar) would do the trick. 
Consider controls over radio.  Anyone can acquire the technical means to broadcast but they don’t due to government control.  That same control could be used to stifle citizen access to the Internet in a time of national emergency.
The answer here is political forces are how government actions are controlled.  The good news is economic forces have converted to political force to prevent the dark vision at the heart of this question.  The bad news is those same economic forces may well push the Internet away from the model we know today to something with even more tracking or throttling based on service contracts or commercial alliances. 
Thus the best answer for the citizen is to exert political force effectively or else prepare for changes beyond their control.

A:

All those nice Internet packets have to go somewhere. In some countries, the government has the power to simply cut off the lines, at which point the game is pretty much over.
The two main countermeasures are:

Use transmission channels that the said government cannot afford to switch off, and does not have enough technology and power to efficiently filter. For instance, a few years ago, there were about 60 thousand Internet users in Syria who were actually using modems over land lines, calling foreign ISPs (I am quoting this figure from memory, I may be wrong; but the principle remains).
Use new transmission channels which are out of reach of the cut-the-wire policy. Namely, satellite internet access. Some countries ban satellite phones, but banning and effectively preventing are two distinct things. It has been reported that Libya jams (or used to jam) satellite phone communications.

(Now I must say that your question implicitly assumes that the said government-led Internet blackout is bad, and that trying to keep Internet access in that situation is rightful, though illegal. This is a controversial issue, to say the least.)

