I have to admit that cinematic excellence is only one of two of my qualifying criteria for sending a film to the troops. And mostly that boils down to "is it good enough to watch again and still find something in it to enjoy?"
The other criterion is personal values. Is there anything in it that devalues soldiers and by extension policemen, etc, and what they do? Is the movie one that will pull the service members down from good ideals, or even better, is it edifying, will it teach them something worth knowing?
Yesterday I bought several copies of The Great Raid to send out. Not because it is a classic, but because it gives kudos to soldiers for a valiant job well done and is a decently made film. Also got a couple more copies of Coach Carter. A hackneyed theme, but well done and a theme worth repeating. (And I never turn down a good movie with a "minority" lead...my form of inverse racism, because a lot of my adopted soldiers are Americans who deserve to see themselves reflected in our hero leading rolls.)
And I got 6 new movies to screen, of which King Kong was the one I was glad I'd rented rather than bought. There is this little dig at soldiers at the end of the movie making them to be jerks for posing in front of the dead Kong, and also giving no value to the airmen who lost their lives trying to protect the city from the dangerous and deadly beast atop the Empire State building.
It's nice to have The Great Raid available now. I wanted a decent WWII film for my history/war category, which I send to enlighten the soldiers about the nature of warfare in the past. Too many people don't realize what a vicious enemy imperial Japan was.
So far in my warfare/history collection that I try to send to all the bases are
Braveheart (Mel Gibson)
Last of the Mohicans (Daniel Day-Lewis, Russell Means)
Gettysburg (Jeff Daniels, Martin Sheen, Tom Berenger)
Lawrence of Arabia (Peter O'Toole)
and now I'm starting to send
The Great Raid (Benjamin Bratt)
The Killing Fields (Huang N'gor, Sam Waterston)
for those not too close to combat
We Were Soldiers (Mel Gibson)
Black Hawk Down
As I haven't found a good movie about the Revolutionary War or the Cold War, I send books:
1776 (David McCullough)
Reagan's War (Peter Schweizer)
I've sent these books on WWII
Winds of War (Herman Wouk)
and
Goodbye Darkness-Memoir of WWII in Pacific (William Manchester),
but there isn't a quentessential book or movie about WWII that I've found; the truth is broken up into pieces that must be gathered together to see the whole of that war.
Any movies about our history with warfare that impressed you?
I've also sent Troy, mostly because of Brad Pitt's sword wielding scenes, and because the seige of Troy and the battles there are historic. In High School we read The Iliad and The Odyssey in Latin, so I missed the gods and goddesses contending with each other, which was part of the epic poems and not in the film, like the image of Hera in her jealous rage personally shaking down the walls of Troy among other visual imagery of Homer.
Your criteria is admirable and I support you wholeheartedly. I believe the following list meets and xceeds your criteria (pretty sure).
Some of my faves:
Guns of Navarone
The Patriot
Glory
Braveheart
Patton**** I love this one!
The Crossing
Gallipoli
All Quiet on the Western Front
Tora Tora Tora
Empire of the Sun
Ben Hur"""" Love it.
Gladiator
Spartacus
Cold War?
How about North by Northwest?
Goldfinger
Red Dawn
Red Heat
Hunt for Red October
May I also recommmend to your the best historian of them all: Paul Johnson and his "Modern Times Revised Edition : World from the Twenties to the Nineties", includes a lengthy section on WWII. Any of his tomes are wonderful and enlightening.