A motor and most chips expect a fixed voltage, and will draw the amount of current they need.
The current drawn by a LED varies over a wide range with only a small change in voltage, and how it changes depends on the individual LED, the temperature, etc. Yet a LED needs a specific current to operate well (give sufficient light without being damaged by over-current). Hence it is not practical to drive a LED with a constant voltage. Instead an LED must be driven by a constant current source. A constant voltage + a series resistor is a crude but workable approximation of a constant current source.
Summary: use a series resistor when your device needs an approximately constant current, but what you have is a constant voltage.