Perhaps one of the greatest if not the greatest depiction of war and military put on screen, Band of Brothers premiered 20 years ago today.
If you've never seen it, go watch it. If you've seen it already, it may be a time to watch it again.
If you want similar level of authenticity (but a very different atmospherics), I highly recommend Generation Kill. While it will never be Band of Brothers, it's probably the best regarding modern day war and military.