A few Things that will happen
1) Greatly reduce accidents, as computers don't get bored/lose concentration/fall asleep.
2) I know several people, me included, that if I could spot a google car would just cross the road in front of it expecting it to stop. Can't see them progressing very well in cities.
3) More traffic as could do other things while commuting, and don't need to care about parking.
4) Private cabs/ taxi reduce in numbers. Car club operators would take over.
5) People start buying motor homes to go to sleep in the back while travelling.
6) Police get IR cameras to find people above.