Yep, Apocalypse Now, is the daddy.I can't be the only one who considers Black Hawk Down to be shite?
Probably far too modern for classic status, but I did enjoy American Sniper. The Pianist, Platoon, Saving Private Ryan, Full Metal Jacket, Zero Dark Thirty all excellent. But Apocalypse Now will always be the Daddy for me.
Honourable mention for Stalag 17, too. (Although it's possibly more of a prison movie).