OPERATION VIGILANT GUARDIAN: The ironically dubbed “Vigilant Guardian” was the first to be widely acknowledged, notably in the BBC’s excellent 2002 documentary Clear the Skies. The exercise, as the official one-paragraph web page explains, was a regular, yearly exercise designed to simulate a “crisis to North American Air Defense outposts nationwide.”  As a result of Vigilant Guardian, according to NEADS Commander Colonel Robert Marr, “The fighters were cocked and loaded, and even had extra gas on board.”  Exact details remain classified, but it was a multi-day exercise, already going on for at least a day as the attacks began.
Three different accounts of first notification of a hijacking indicate that there were to be simulated hijackings in at least Vigilant Guardian: Major General Larry Arnold said “the first thing that went through my mind was, is this part of the exercise? Is this some kind of a screw-up?”  Sergeant Jeremy Powell at NEADS, where Vigilant Guardian was being carried out, was contacted by Boston Flight Control at 8:38 am. The Boston controller told him there was a hijacked plane headed to New York. Powell responded “is this real-world or exercise?” He received the answer “no this is not an exercise, not a test.” 
The most relevant account is that of Lt. Colonel Dawne Deskins. As NEADS regional overseer of Vigilant Guardian, she should have understood better than anyone what to expect from the drill. Newhouse News Service reported her response to the crisis: "At 8:40, Deskins noticed senior technician Jeremy Powell waving his hand. Boston Center was on the line, he said. It had a hijacked airplane. “It must be part of the exercise,” Deskins thought. At first, everybody did. [After clarifying with FAA] Deskins ran up a short flight of stairs to the Battle Cab and reported the hijacked plane real world, not a simulation.” 
Name Meaning: “Vigilant or Amalgam means it is a HQ NORAD sponsored exercise. Guardian means it is a multi-command CPX, or command post exercise (no live-fly). So on 9/11, NORAD was conducting a NORAD-wide, multi-command, command post exercise with no live-fly." - Major Don Arias, NORAD press spokesman who was on duty and involved in the response the morning of 9/11, to Mike Ruppert. As reprinted in Crossing the Rubicon, page 368.
(the original page had this quote, but by 2006 the page makes no mention of a crisis but explains it is now "conducted in conjunction with USCINCSTRAT-sponsored GLOBAL GUARDIAN and USCINCSPACE-sponsored APOLLO GUARDIAN exercises. The exercise involves all HQ NORAD levels of command and is designed to exercise most aspects of the NORAD mission.")
 Scott, William B. “Exercise Jump-Starts Response to Attacks.” Aviation week’s Aviation Now. June 3, 2002. Accessed April 27, 2003 at: http://www.aviationnow.com/content/publication/awst/20020603/avi_stor.htm
 ABC News. “Terror Hits the Towers: How Government Officials Reacted
to Sept. 11 Attacks.” September 14, 2002. Accessed at: http://abcnews.go.com/onair/DailyNews/sept11_moments_1.html
 9/11 Commission Final Report. Page 20
 Hart, Seely. “Amid Crisis Simulation, 'We Were Suddenly No-Kidding Under Attack.'” Newhouse News Service. January 25, 2002. Accessed May 7, 2003 at: http://www.unansweredquestions.org/timeline/2002/newhousenews012502.html