Whether it's the greatest can be debated, but I have to throw "Tae Guk GI' out there. Definitely among my favorite war movies of all time.
If you haven't heard of it (which, I'm sure you haven't), it's a Korean-made movie about the Korean war. Best viewed in the original language with English subtitles, seeing/hearing it in English first kinda takes away from the emotion felt the first time through.