I agree with most of the posters here that the market for Uber totally replacing household vehicles is pretty slim. However I think there could be a larger market for Uber replacing 2nd/3rd vehicles.
That said, there are already taxis and car share programs. Uber may be able to take customers from them but I'm not sure that Uber really provides something compelling enough that it would push a large number of people who are at the margin over the edge. Disclaimer: I've never actually used Uber
Uber definitely provides a significant improvement over taxis in pretty much every way. Day to day use of taxis in most jurisdictions is pretty much impossible because, if this is even possible, they are even less reliable than public transportation.
With a taxi, unless you're going from a dense main drag (of either people or taxi-needing people, ie. bars) you call for a cab and it may or may not come some time between now and 2 hours from now, depending on if the cab that's supposed to pick you up got flagged down for a better fare.
And then, in most places, the cabbie will tell you he can't take anything but cash. After some grumbling they might let you pay with a credit card, or they might make you take them to a cash machine.
With Uber you say you want a car and it tells you where the car that's coming is and how long it'll take to get to you. And then when you get there you pay by clicking a button.
That said, there are already taxis and car share programs. Uber may be able to take customers from them but I'm not sure that Uber really provides something compelling enough that it would push a large number of people who are at the margin over the edge. Disclaimer: I've never actually used Uber