Imagine a future where cars are not owned by individuals but are owned by few companies (or maybe even government, the way public transport is) and participate in what is essentially a global taxi network.
Instead of using your own car you would just step out of your home, enter destination address into your phone and press a button. That would be sent to a server which given your location, position and destination of all existing cars in route would pick one that is the closest to you that has available seat and goes in that direction. That car would just pull up and you would be notified in real time how far it is from you.
If a car is not available, it would be dispatched from the closest holding area.
Think ZipCar except with cars that come to you, drive themselves and you can share with other people while it drives itself (or you can have it for yourself, if you prefer, except at a higher cost).
This kind of a network would drastically reduce number of cars needed to drive people around and given global knowledge of where people are and where they want to go, it could plan the absolutely most efficient route.
For popular routes (e.g. if it detects a pattern that a lot of people commute from San Francisco to Mountain View around 9 AM on Mondays through Fridays) it could deploy bigger cars (i.e. buses), further reducing traffic.
When you think about it, it's not surprising that car companies will not work on a technology like that since it would drastically reduce demand for cars and if this comes anywhere close to reality, expect lots of legislative and political battles (after all, this will mean that Americans in Detroit will loose jobs).
What's so beautiful about it is that it takes a massive infrastructural liability -- a century of building our world around the automobile instead of around rail or other mass transit systems -- and turns it on its head. We get out of infrastructure jail free.
Think of the time humans spend behind the wheel of a car today. How many hours a day? How many solid days of driving a year? How many man-years of humanity are wasted on fruitless idling in traffic? A society with autonomous personal transport becomes a measurably more productive one and likely a happier and more satisfied one as well.
Car companies may fight it but it won't matter, the economics are overwhelmingly against them on this, because signing up for this service will be overwhelmingly cheaper than owning your own car, probably by at least an order of magnitude for most people.
Random digression, but I think you will find this is an NP-hard problem - I'm quite sure you can encode the Travelling salesman problem[1] within it. So the absolutely most efficient route is probably not feasible, although the system could certainly do a good job optimizing over what we have now.
[1] http://en.wikipedia.org/wiki/Travelling_salesman_problem
Personally I view mass transport as the stop gap to deal with the fact that cars really suck today. Mass transport will never be optimal because (a) it is mass transport, which means sharing space with a bunch of (potentially sick) strangers and (b) the bigger the group the less common the final location. A car can go exactly from point A to point B but a train can only go between stations. Every change between train (city-to-city) to tram/bus (location within city) is wasted time, as is every tram/bus stop that you don't use.
In my perfect world we would get rid of mass transport and just have a sort of network of cars. Most trips people take are planned well in advance so you could schedule when you want to leave, walk outside and step into the car that's waiting there for you, kick back and wait to be let out at the door of where ever it is you're going. The car wont need to park because when it's done with you it goes for the next person.
Something like this would be much more efficient than mass transport that has to just keep on making the same trips regardless of how many or how few people are using it at those times because people might need to use it.