Saving Private Ryan has to be my all time favourite - for not only the plot line but the realism.
Band of Brothers isn't a movie but a TV series so it doesn't really count but it too rocks for the realism and the authenticity of the equipment used.
I dislike war movies that ruin the realism e.g. The Battle of the Bulge (that used american tanks thinly dressed up as panzars). Even many Vietnam movies are guilty of this, e.g. using Twin Huey's (a twin engined Huey Chopper introduced in 1968) for pre 1968 Vietnam scenes.
For me War films have to be accurate to the 'T'.
Platoon and Apocalypse Now (esp the Redux version) are also on my list of great war movies.
A bit of trivia - Full Metal Jacket a film of the Vietnam conflict was filmed entirely in Britain-
Like most of Kubrick's films.
http://en.wikipedia.org/wiki/Full_Metal_Jacket
And the series Band of Brothers was also filmed entirely in Britain (not by Kubrick of course).
And a movie that I laughed myself silly was Good Morning Vietnam. Watched the uncensored version in Msia on rental video before it was released in Sg back in 1988. The version shown in the Sg Cinemas was so cut up and sanitised it wasn't funny anymore (not that the original was that "crude" to begin with). Can't believe they actually dubbed over the word 'pissy' to something else. The movie didn't do very well in Sg bec not many people got the jokes. You have to know a bit of american military lingo and history to get some of the jokes. e.g. KP = Kitchen Police (soldiers assigned to kitchen duties like peeling potatoes - usu as punishment - like having to do guard duty for us in the SAF).
Women esp will not appreciate this movie very much.