An incident is simply an event or something significant that has happened. A scandal, a misunderstanding or a fight can be an incident. An accident is something that shouldn't have happened. If you crash your car into a lamppost because you weren't paying attention to the road, this is an accident. Spilling your coffee on your schoolbooks is an accident. Getting pregnant can be an accident if you weren't intending for this to happen. (Sorry to lower the tone.) Not all accidents are incidents and not all accidents are incidents. A small, insignificant accident (such as spilling your coffee) is not an incident because it isn't very important and doesn't affect many people. A plane crash is an incident, but it may or may not be an accident. If the pilot made a mistake with the controls, the crash was an accident. If the pilot was a terrorist or a psycho (or both), the crash was not an accident. But it was still an incident.

Very good question! They are certainly somewhat interchangeable but not always. In the US car crashes are referred to as accidents. An incident can be large or small but is usually a broad reference to some sort of unexpected, unwelcome event.

Sorry...the middle sentence should have been this: "Not all accidents are incidents and not all incidents are accidents." I wrote the same phrase twice. This was an accident - not an incident :)