Google has apparently been testing unmanned cars with some success (link).
I suspect biggest impact of unmanned cars would be taxi services replacing private ownership of cars. I would guess that the biggest differential cost between private car ownership and taxi services is the need for a non-passenger driver; human labor is expensive. If you eliminate this cost for taxis, it would become much more practical to call up a car and have it come pick you up when you need to go somewhere instead of keeping your own car around. Unmanned taxis would also eliminate a big fraction of the need for street parking, since cars could be kept in central parking garages. This would increase space efficiency in medium sized cities quite a lot.