Cars will become less powerful as they are vastly overpowered for most needs now, and they will become fancy living rooms on wheels. The seats may all face each other, entertainment systems will become a major focus of design, built in beds, etc. You get in a car, tell it were to drop you off, it then self parks somewhere and you use your cell phone to tell it where to pick you up.
Trucks will become driverless vans, the same as all delivery type vehicles although some may still have passenger space for workers to help load and unload cargo. Pizza delivery vehicles won't even be cars, but little heated boxes on wheels.
No traffic signs, guard rails, lines on the roads, probably many other changes would be possible as well.
In areas with pedestrian traffic the walker has to push a crosswalk button, which would then broadcast a signal to nearby cars to stop or be aware of the pedestrian in the street and the walker could cross with very little delay. Run into the street and get hit - it's probably your fault.
Cyclists would carry little transmitters which would let nearby cars know it's location and velocity, allowing the cars to give the appropriate allowance to them. This is if they are sharing road space.
Rates would drop by a huge amount and after a time of vetting they might even go away or become a small part of the purchase price of the car.
This is just a start, the changes to society would be huge, the number of deaths would probably be in the 10s or 100s per year in the US if all vehicles are automatic instead of the 10s of thousands. I know several people who have been killed or seriously injured by vehicle accidents and would be very exited if/when this technology comes to bear.