Many single phase AC motors have one. Universal AC motors that can also run on DC don't. And three phase AC motors don't.
http://www.whelco.com/AC_Motors.html
AC motor types:
Single-Phase Induction Motors – are more common than all the other types put together. They are the least expensive, lowest maintenance motors available. They are used in countless residential and commercial applications. They are typically fractional horsepower units used where three phase power is not available. This motor has only one stator winding and operates on a single-phase power supply. The rotor is always a squirrel cage construction. There is a main winding and an auxiliary winding for starting the motor which is disconnected by a centrifugal switch when the motor reaches about 75% of synchronous speed. Generally used for applications up to about 3/4hp.
