It is my belief that the spread of car sharing smartphone apps such as Uber and Lyft will drive a decline in taxi cab use over the next 5 years. The convenience and quality of a ride from a car sharing app easily surpasses the taxi experience. Instead of dealing with sometimes rude and dangerous cab drivers, riders will prefer the ride of Uber drivers who drive clean, well maintained vehicles and treat customers well.
The use of taxis can decline as long as people are using other forms of public transportation such as busses, trains, subways and trams. In my town we do not have any taxis at all. You either own a car, you walk or you ride a bicycle. In bigger towns the use of taxis can
Taxi cabs are only prevailing today because of the barriers to entry that have sprouted up in the form of legislation and regulation around the industry. Taxi cabs are slow, typically have difficult and unpleasant drivers, and don't provide a great offering for the consumer. There are a lot of tech companies out there today providing a much better offering to the consumer and are willing to throw in the legal expense it will take to unbar that industry.
While in small towns taxi cabs are already pretty much non-existent, they are still widely used in big cities, and I don't think it is likely to change. It's a convenient way of getting to places. Not everyone is obsessed with always driving a car, and driving in a large town is far from fun. Also, there are lots of travelers who come in by air, so they don't have a car with them and not necessarily wish to rent one. So, I think taxi services are here to stay.