for whatever reason, one of the first things that comes up in proposing the abolition of the state to someone who is new to the idea is who will build roads if there is no government to do it. it's really pretty funny how this question is automatically the first thing that most people ask.
as with virtually any question requiring one to prognosticate on what would or wouldn't be in the stateless society, or a purely libertarian, anarchic society, the best answer is "i don't know". because, let's face it, when the creative genius of the populous is unleashed without restraint, no one can ever know what solution they will come up with for various issues. that being said, i think it is at least somewhat safe to make some educated guesses on the way things may look in such a world.
i've made posts in the past concerning the issues of regional defense and justice. the difference between those topics and this one is that those were centered on services rather than goods. i find the "roads question" slightly different and more interesting.
to get right into it, there are many ways in which the market may supply roads. first, it should be recognized that means of transportation are an essential element to any advanced economy. as such, the demand for them will be high. perceived demand is always the first building block in deciding whether or not to dedicate resources to production. because of such demand, there are people who have expertise in building roads. obviously this is so, because roads exist. often, these roads are built by private companies that are enlisted by governments to build. so, if the state were to disappear tomorrow, would those companies say, "well, the government's gone, so i guess we'll just close our doors, go out of business and starve to death, even though there is massive demand on the private markets for our products"? would consumers say, "well, the government's gone, so i guess we'll just use these roads until they fall apart, then go back to living the pioneer lifestyle because we can't trade in the complex economy without a means of transportation, even though there are companies out there with the wherewithal to build perfectly good roads"? would entrepreneurs say, "i see lots of opportunity out there to make money getting road builders and road consumers together, but instead, i'll just not make money and enjoy living in an economy that is only capable of providing the bare essentials since it has no transportation infrastructure"? of course they wouldn't! supply would go where demand led it and people would pay for the things they need and entrepreneurs, in the process of competition, would insure that things were done in the cheapest, highest quality way that suits the needs of the consumer, just like they do in every other sector of an economy (at least those not dominated by the state).
roads could be supplied by road companies on a subscription basis, or by companies needing them for shipping and allowing citizens to travel on them for the sake of advertising, they could be toll operated, advertising supported (this road brought to you by the ford motor company, for example), or any other configuration that i can't even think of. competition in the markets would make them safer, cheaper and more accessible. they wouldn't be laid out in the irrational manner in which they are now by central planners. they would have to go where people really wanted them to, in order to maximize profits and minimize wasteful resource allocation.
in my opinion, how roads would be provided is a good question, but a better one is, "would we still be using roads?" one of the side-effects of governments entering markets like the market for roads is that they are able to drive out competition by accruing to themselves a zero cost basis. because they don't have to do anything well in order to receive funding (they simply take what they want by force through taxation), they make it impossible for legitimate firms to compete. they force people to pay for the roads they build and then people have to pay extra to afford the offerings of private firms. because of the expense involved in anything the government does (they don't have to be economical because they have unlimited access to forced funding), their very expensive roads make it difficult for consumers to afford to pay for private roads on top of reducing the incentive to do so.
after private businesses are driven out of the market, the state's monopoly begins to run its usual course of providing low-quality goods and services at a high price. because the government has no competition, there is little incentive to innovate and no process of market input to determine how such innovation should be implemented. what we end up with is road technology that's stuck in the era in which the state overtook the market. if roads had been market provided over all of these years, there's no telling if the innovations forced by competition would have gone so far as to eliminate the need for roads entirely. we might be flying everywhere, or have moving belts for travel like you see at airports for pedestrians. there's no way to know what we're missing out on when it comes to travel because of the interference and outright crippling of the market process in this area.
there's no need to fear that without a government there would be no roads, in fact there's everything to look forward to in the exciting innovations the market would surely create.