Master and Commander, with Russell Crowe, Paul Bettany. Great action scenes at sea, but also examples of good and bad leadership in naval life that resonate today. Not a "great for the ages" film, but most enjoyable.
U-571, with Harrison Ford and Liam Neeson. Will bring new-found respect for submarine life, as well as an appreciation for the political pressures that can put military lives at risk.
Glory, with Matthew Broderick, a young Denzel Washington, Morgan Freeman and a big-name cast. One of my all-time favorite movies. Admit it makes me cry every time.
Oh, and Heartbreak Ridge, with Clint Eastwood. A classic hard-bitten Marine with heart of gold story, with some good comic moments along the way. You get some sense of the pride of being a Marine.
Did you catch Game of Honor, the recent Showtime (I think) documentary about Army-Navy football? I still see it showing.
Of course, anyone who has served can pick the heck out of military movies, the things that just aren't true, right or done just for the dramatic effect. That doesn't mean they aren't enjoyable overall.