Tragedy of the commons. Simple solution: congestion prices. Singapore is an example. Any others?
The 91 Express Lanes (http://en.wikipedia.org/wiki/91_Express_Lanes) in Orange County are an interesting case - instead of charging a fixed toll to enter an area, there is a variable toll on a 10 mile stretch of freeway. There are 4 free lanes in each direction and 2 reversible toll lanes that go with the rush. Tolls vary from free (at night) to $10 on Friday afternoon.
One concern about these variable toll lanes is that they would only be used by the rich, but studies of license plates of drivers showed that every demographic used them about once a week, rather than every day or never. Pretty cool what happens when people have the option to pay more for better service.
PS: There is a reason you can get an International Driver's License.
But also: a trend in traffic control is to reduce the markings, so that people pay closer attention, using their innate intelligence to drive cooperatively. (The idea goes by the names 'psychological traffic calming' or 'naked roads'.) Speeds go down a little; accidents go down a lot. It seems traditional markings lead to overconfidence -- a destructive abdication of personal responsibility to the authoritative sign-makers.
So even if a patchwork of private roads couldn't agree on any signage standards, and just tore out all the signs (as the safest, liability-reducing option), we might wind up better off. (But of course, freeways and major thoroughfares/intersections would just work the same as they do absolutely everywhere else, under any ownership system.)