This already exists in Austin, TX and a few other cities around the world. http://www.car2go.com has Smart cars scattered around the city. You grab the nearest one (or book ahead with your smartphone), swipe your RFID card, drive as long as you'd like, and then leave it in any public parking spot.
The driverless bit is what makes this work. If I just hopped off the high speed rail from Atlanta to Austin (I'm optimistic!), I don't want to have to walk to the nearest Smart Car center. I want the car to come to me. :)
Edit: Minus the driverless bit obviously. :)