Do motors need to have capacitor even if being used with motor shield I'm using a 12V DC geared motor with an Adafruit motor shield which is connected to Arduino.

So, I want to know inspite of using the motor shield, do I need to add capacitors to the motor?
If the motors have a lot of "brush noise" you need to add capacitors to the motor. It is written in the FAQ.

The noise must be suppressed at the source or the motor leads will act like antennae and broadcast it to the rest of the system link.