Exclaimation used when one specifically does not want the shotgun seat in a car, most often in a cab. The last person to call "notgun" has to sit upfront with the cabbie and will most likely get stiffed with the fare.
"Ha ha, Lance forgot to call notgun and is now stuck upfront with the cabbie. Let's stiff him."
This should be used in place of shotgun not. It used when you are with a group of people and you don't want to do something, with 'notgun' coming before the action. The last person to not call 'notgun' has to do this action.
Dave: Notgun ordering the pizza!
Fred: Notgun ordering the pizza!
Jane: Notgun ordering the pizza!
Paul: Shit, there's no-one else here, I guess I have to order the pizza...