The Thin Red Line is probably my favorite war movie because it deals with the effects of war on combatants in a much more personal manner than most others. It has its fair share of blood and guts, but its introspection helps you understand the emotional toll war can take on its participants and their loved ones.
I'd also recommend Band of Brothers for this same reason. Great character development too. It takes a few episodes to warm up, but the combat footage is pretty intense; almost a direct reflection of Saving Private Ryan (not surprising considering it was produced by Tom Hanks and Steven Spielberg).
Black Hawk Down is a bit short on substance, but with the events having taken place much more recently, the characters are more identifiable because they embody our modern sensibilities. By the way the soldiers talk and interact, you realize that these really are just kids we're sending into battle. The technology is more recognizable as well. I think these things help modern audiences identify with the material a bit more than films about wars in the past.
Classics include Patton and Full Metal Jacket (just for the bootcamp scenes alone).
Don't bother with Windtalkers. It's reminiscent of older war movies that were more gung-ho about combat so it doesn't stand up to the stark realities presented by modern war movies. Some of the action sequences are downright Rambo-like, with Nick Cage taking out entire squads armed with automatic rifles using nothing but a pistol. I was never a fan of John Woo because his movies really push the limits of suspended disbelief, and applying his style to a war movie leads to something pretty ridiculous.