I predict one of the first things Google will do with self-driving cars is automate the trucking industry. This will be a huge change in terms of improving shipping efficiencies, but I do not believe that it will fundamentally disrupt the logistics industry: at most trucking companies, the turnover rate for drivers is over 100%. Truck drivers are already treated like robots.
The current passenger automobile system, on the other hand, will undergo a complete and total change.
Self-driving cars will lead to an almost complete elimination of both privately owned cars and public transportation in cities. Robot taxis will become so cheap and ubiquitous, and parking space so expensive, that it no longer makes sense to own your own car (many residents of NYC and San Francisco already find parking unaffordable today).
The first step to this is already being implemented - the automation of taxi dispatch.
Robot cars are safe. The auto insurance industry will be virtually eliminated.
Robots cars need less maintenance and will refuel themselves. Most gas stations and service shops will be consolidated into a few large service depots.
A city will have less automobiles but its citizens will use cars more often - even with peak demand, a smaller fleet of robot taxis than private vehicles can service commuter needs.
Self-driving cars have better road capacity utilization, so even with increased automobile use, the amount of paved roads in cities will be reduced, as unused lanes are reclaimed for real estate development. The same thing will happen to parking lanes and lots - even as demand for parking goes down, the price will rise as the parking spaces get reallocated to more profitable real estate development and the supply shrinks at a faster rate. This will have the effect of greatly reducing road maintenance expenses and increasing property tax income for city governments.
The layout of cities will return to the pre-automobile era, the most visible changes being narrower streets.
On the other hand, the highway system will face pressure to expand, as robot taxis will undoubtedly be used as a substitute for air, train, and bus travel. Robot taxi operators will be national or even international in scale, and who cares if a particular robot taxi was working in New York yesterday and is in Chicago today, as long as on average the operators' fleet utilization is maximized? The key ability of self-driving cars to link into aerodynamic paceline "trains" (much like bicycle racing teams) will make long-distance fuel consumption competitive with trains and buses.
The robot taxis by themselves will also be much more aerodynamic than today's cars. With the elimination of private ownership, automobile body design will no longer be driven by the status symbol desire, but by taxi operators' need to minimize fuel consumption.
What does this mean for public transit? Buses and street-level tramways will be out, but subway networks will likely remain viable because subways are not vulnerable to traffic jams and snow.
In terms of traffic, it is likely that the top speed of a journey will decrease, while the average speed increases. Robot cars can potentially negotiate intersections much more effectively than human drivers. Congestion at peak times will likely still be a problem in city centers due to decreased road capacity, but the traffic jams are likely to be shorter and involve higher average speeds.