In many cities around the world, taxis are heavily regulated. Among these regulations are a fixed number of license plates, and the costs of these plates (or equivalent medallions, etc). This means that in many instances there aren't enough taxis to go around because these numbers were fixed a long time ago and may not be have been updated to meet demand. This benefits most the taxi operators and to some extent the drivers themselves because a high demand drives the price of the fare up. Also a business with low competition is always more comfortable to run. Customers hate it but are used to this situation.
Now Uber and others have sought to change the game, first by ignoring regulation and getting self-employed people to drive their own car to ferry people around. This is very good to some extent because taxi business in a lot of places is over-regulated and does not meet demand. Also the Uber et al have a nice online presence and at this stage at least do provide a useful service, so why not.
However, Uber fares are not cheap, this is not "sharing", this is a business. The self-employed individuals driving the cars may be putting themselves at risk: with their rides, the regulatory authorities, in case of accident, with other regulated taxi drivers, etc. We are still in a "honeymoon" period but this is sure to end. Uber has become much to big to be ignored, and so will soon have to fight for its own existence, in a lot of places all at once. I'm not sure their (huge) valuation will be enough.