Aesop corrects the list posted by Art Of Manliness. His is a good list. I offer these quibbles because, well, you know how I am ...
Glory. What I think is best about this film is how the Fort Wagner scene captures the how the troops knew they were likely doomed, but fought anyway. This scene transcends the obvious "racism bad, mkay?" that hits you between the eyes all through the film - and for once the black soldiers were just soldiers. And yeah, Denzel was pretty awesome.
Stripes. Comedy doesn't get any respect in Hollywood (scan through the list of Bet Picture winners if you don't believe me). But the Queen Anne's Drill scene in this film makes it the best military comedy filk ever made.
Band Of Brothers. Not a film, but made for TV - but simply the best made for TV military show ever made. It's so epic that people make Lego stop action scenes from it. Srlsy:
And if we are talking "epic", we need a shout out to John Banner for his portrayal of Sgt. Schultz in Hogan's Heroes which has become part of the modern vernacular. Sure, it's TV and it's comedy, but it's still epic.
As I said, these are quibbles and you should go read Aesop's list. I agree 100% with his choice of Zulu as #1 - and ASM826 posted a great review of that film last year.
UPDATE 30 May 2021 15:01: Dwight weighs in. Well worth a read.
UPDATE 30 May 2021 23:09: Adam Piggott also weighs in, and brings in some films that others hadn't. I have to agree that Ran should be on the list. And comedy gets if not respect, then at least a head nod from him with Kelly's Heroes.