I will kick the topic off by mentioning a classification of means for providing protection against external aggression, as enumerated by Roderick Long in the highly-recommended Anarchy and Law collection.
He suggests looking at four potential means:
1. Profit-based corporations providing defence to paying clients. Such solutions are often offered by libertarian thinkers, and most often criticized based on free-rider or public-good concerns. In my opinion, such solutions can work very well in defending single-owner, high-value targets such as industrial installations or major banking centres (where gold and silver are actually stored). When a given geographical location is not single-owner, but is very high-value and is either owned by a small number of organizations, or where defence is motivated by a small number of actors, for-profit defence can still work. For example, the down-town of a major metropolitan could be insured to a high amount by a handful of major insurance corporations. Those could work together to provide military defence, thereby reducing risk and, with it, their potential liability.
2. Charity-based solutions. The UK has spent significant resources defending the Falkland Islands from threats by Argentine. The UK is a democracy, and, presumably (and probably supported by polls), most British voters don't mind having their tax payments diverted in part toward providing such defence. Similarly, Americans broadly feel good (whether justifiably or not) about providing military support out of their tax dollars to a variety of countries around the world. There is no reason to expect people will change their priorities just because they are no longer compelled to make those payments personally. In other words, people may well contribute funds towards the defence of others.
Charity could come both from within the free society, and from without it.
3. Self-help violent defence. A free society is likely to be much better armed, as any gun-control laws could only be local and rational. Further, a free society is likely to be much more prosperous and wealthy. A free society living under the shadow of a foreign threat would have its members divert more of their income towards acquiring defensive measures. It is easy to see individuals armed not just with automatic weapons but also with anti-tank and anti-aircraft missiles. Who knows what a competitive market in high-end personal weapons might come up with. Invading a region with low concentration of attractive targets (as most residential and farming areas are), but with well-equipped and highly-motivated local population could be a very bad idea indeed.
Such self-help could easily be organized in a bottom-up militia structure, as has been the case, for example, during the American Revolutionary War.
4. Non-violent defence. Much has been written about the value and power of non-violent defence against state aggression. Even under Nazi occupation, non-violent methods were used by the citizens of several countries (Denmark, Norway) to successfully protect and evacuate their Jewish populations. Contrast that with the abysmal failure of governments to provide similar defence.
To those four means, one must add the peaceful and cooperative nature of a free society - one naturally engaged in trade and population exchange with its neighbours.
The combination of low-threat and diverse defence mechanisms should be contrasted against the decidedly mixed records of governments in providing for the defence of their subject. The free society could easily come ahead in any such comparison.
Government is not the solution. Government is the problem.