Source: www.imdb.com

No mystery. I picked out a few examples. Also, I bet the information at imdb is very incomplete.

Selected film and television titles

• Man of Steel (2013): Department of Defense, U.S. Army (films go back to 1911 in the list), North American Aerospace Defense Command (NORAD), etc.
• Argo (2012): Central Intelligence Agency (CIA)
• Transformers: Dark of the Moon (2011): Department of Defense, 45th Space Wing, National Aeronautics and Space Administration (NASA), United Nations, etc., etc.
• Iron Man (2008): Department of Defense
• Stargate: The Ark of Truth (2008): Department of Defense, U.S. Space Command, Department of the Air Force
• “24: Day 5: 5:00 a.m.-6:00 a.m. (#5.23)” (2006): Department of Defense
• The Core (2003): Department of Defense, United States Marine Corps, Department of the Navy, etc.
• “The West Wing: In Excelsis Deo (#1.10)” (1999): Department of Defense
• Saving Private Ryan (1998): Department of Defense
• The Jackal (1997): Department of Defense
• Air Force One (1997): Department of Defense, Department of the Air Force, Department of the Army, etc.
• The Silence of the Lambs (1991): Department of Defense, Federal Bureau of Investigation (FBI)
• Star Trek IV: The Voyage Home (1986): Department of Defense
• Firefox (1982): Department of Defense
• Gray Lady Down (1978): Department of Defense
• “The Twilight Zone: The Last Flight (#1.18)” (1960): Department of Defense
• South Pacific (1958): Department of Defense
• Animal Farm (1954): Central Intelligence Agency: “(funding) (uncredited)”
• Fighter Attack (1953): Department of Defense
• Courage of Lassie (1946), Quartermaster General, Army of the United States

Acknowledgements: Jay Dyer and HoaxBustersCall.com re. Twilight Zone episode especially, also Alan Watt.