This is a short post, if only because this is a simple idea.
Right now, all roads, as far as I know, are maintained by private companies, but governments pay for those companies to maintain the roads. The same thing occurs as far as how the military gets its weapons; companies build the bombs and bullets, while the government pays for those bombs and bullets to be made.
The difference between public and private roads is who pays for the roads. If you want roads, you will pay for them; why should those that don't use the roads pay(be taxed) for them?
If governments were to (1) stop paying for roads and were to (2) stop regulating roads, then individuals, companies, and communities would pave and maintain roads as they see fit. This would be organic and decentralized, rather than planned and centralized; it is no wonder roads are terrible everywhere I seem to drive, except in my apartment complex, driveways, and parking lots.
Also, I've come up with a proverb (if it can be called that):
Private property is the basis of prosperity; politics is the basis of poverty.