I had a poll up to ask what services should only the government provide.
Some of the popular choices were fairly uncontroversial: defence, police, courts, embassies, border control (although a libertarian society would be much more relaxed about borders than we are) and prisons.
Oddly enough, external spying was seen as a popular choice and I suppose that you might make a case for it on the grounds of defence. However, if you can make a case for external spying, then I can't really see why you would believe that there is less of a case for internal spying.
The coastguard is another popular choice, although in its current form it's as much use as tits on a bull.
Regulators were an unpopular choice, possibly because they are so fucking useless in their current incarnation, but also because libertarians believe in an unregulated market. However, even in an unregulated market, you need to have some form of protection against predation or fraud. And that protection must have real bite.
I was baffled as to why more people felt that motorways should be provided by the government than local roads: motorways are relatively easy to toll (just ask the French!) but local roads are much more difficult to make "pay per use" - local roads are something I believe would be more efficiently "provided" by government, even if they sub-contract out the actual work.
Perhaps I should have phrased my question differently or more clearly.