The Story of GI Joe is a fantastic movie. For a film released in 1945 before the war actually ended, it is surprisingly frank and adult. One of Robert Mitchum's best performances, and if you only know Burgess Meredith through the Rocky movies and the 60s Batman TV show, you need to see what a great actor he really was (also check out Of Mice and Men).
William Goldman wrote an article in Premiere magazine pretty much shitting all over Saving Private Ryan when it came out (it's collected in his book The Big Picture), and I agree with everything he said, but I still think the battle scenes are fuck awesome. Band of Brothers turned out to be everything SPR wanted to be - can't wait for that to hit Blu Ray this year (so goes the rumor).
If you haven't seen it, They Were Expendable is another good war flick filmed during the war which takes a pretty realistic approach for the time.