Many of these already mentioned but thro in my 2 cents…
Saving Private Ryan, Iron Cross (German show), I have a soft spot for Bridge over Remagen, A Bridge too Far, White Tiger (Russian film as much supernatural horror as war), Das Boot (another German one), All quiet on the Western Front (I think the original 20s B&W was best), Casualties of War (more of a moral/ethics than war but still war), Kellies Heroes (more comedy but still a war show), Red Badge of Courage (older show and message probably won’t age well to today but still one I like), Platoon, Glory, Zulu, Patton, Full Metal Jacket, Spartacus (another older one), The Hurt Locker.
What can I say, I like war movies 
My wife’s ‘favorite’ (she is an army vet) is Blackhawk Down…but refuses to watch it again.
I have to plug Casualties of War again as I think it has been lost to time. I think you also have to be in the right demographic state and time to get the full effect. I saw the show as a young Buck full of vim and patriotism and the show drug me along PERFECTLY with the full effect of serving your country and loyalty to your buddies and your leader who WAS a great war leader who would and did risk his life for you and was good at his job…to realization that the moral consideration should outweigh this…I was drug along PERFECTLY through this…I could easily have been the Micheal J Fox character going through this. One line still sticks with me after all this time. Something like “Everyone acts like that since we can be blown away at anytime and that nothing matters. I am starting to think that what we do …it matters a lot…more than we could possibly imagine”. I think that show actually had a permanent effect and shift of my morality and view of the world.