Most commonly used? It is closely followed by Permanent Magnet motors. Each has its own advantages and disadvantages.
For example, permanent magnet motors offer high power density and high efficiency. These motors can be very costly and may also experience problems like demagnetization if the temperature exceeds that of the curie point. Permanent magnet motors are used in the Nissan Leaf motor.
However, Induction motors are cheaper to produce and maintain than Permanent Magnet counterparts. They also have lower efficiency and power density. The Induction motor is used in the Tesla Model S.
These two are not the only options. There is also a Synchronous Brushed motor, which Zero Motorcycles uses if I am correct) and a Switched Reluctance Motor (used in Holden/ECOmmodore).
This paper contains a lot of information that you might find interesting.