Apocalypse Now...also the most watch movie from my collection. There is a literary connection: use to be a huge Conrad fan. Deer Hunter would be a distant second.
My favorite is We Were Soldiers. The Deer Hunter and Full Metal Jacket are incredible movies, though. Forrest Gump also deserves a mention for being a fantastic movie in which Vietnam plays a significant role, even if it isn't the whole movie.
Heaven and Earth was an underrated movie to me. It was the 3rd movie in Oliver Stone's Vietnam trilogy (Platoon and Born on 4th of July the other 2).