You guys need to see some of the classic World War 2 movies, like The Longest Day and The Great Escape. You simply can't go wrong with those. Also try Guns of Navarone, Kelly's Heroes, Destination Tokyo, 60 Seconds Over Tokyo, Where Eagles Dare, Battle of the Bulge, Battle of Britain, etc. Plus I saw a Chinese movie recently called The Flowers of War, that was just incredible. There is also this Korean movie called My Way, that was absolutely epic and fantastic. And I can't forget Grave of the Fireflies, if you like anime, just keep the tissues handy.
By far, Saving Private Ryan. It is such a great film, and it really is emotional. I highly recommend it!
Did anyone mention "schindler's list" ? This is probably the best holocauste movie I have ever seen. And the best part is none of the incidents in it are fake. Its all based on true events.
Black Hawk Down is such a great movie and is one of the few movies that I watch over and over again. However, one movie I like that isnt included on your list (maybe its not warrish enough) is Red Dawn. Epic!
The old black and white ones are the best. Stalag 17 was awesome. However, overall I'd have to say that 'Where Eagles Dare' with Richard Burton and Clint Eastwood is my favorite.
Whaaaat? No Mel Gibson flicks on there? The Patriot and We Were Soldiers were both pretty awesome war films. Certainly better than Black Hawk Down anyways.