If it is the EGR, beside the light in the dashboard, you may experience loss of power, slow acceleration, the engine does not run smooth. All these happen if the EGR broke in the open position. This means that nomather what, some of the exhaust gas is pushed back in the engine. If the valve was closed when it broke, than there will be no apparent symptoms. The engine will run smooth. That's why some choose to delete this valve.
If it is the cut-off flap, the symptom is a judder when turning off the engine. Also, if you are unlucky enough to blow your turbo, the oil that lubricates it is drawn in the engine, the engine will rev up and you won't be able to switch it off. This would be disastrous.
@Smoothie: The thread was opened in the 8L section than it was moved here.