There are a few that really to mind.
First, there's the last thirty minutes of With Honors, a 1994 film about some Harvard students who, basically, let a bum into their lives. Very few movies put a lump in my throat like that one did.
Next, Breaker Morant. The final scene is extremely moving, though not so much in a make-you-cry manner; it's simply a very powerful moment.
Saving Private Ryan had several; the breakdown of the German prisoner as he begs for his life- a very difficult scene for me to watch, even now- and the opening scene at the cemetery where the old man breaks down over the grave of... someone.
We Were Soldiers has three that really stand out. The officer wives going from home to home with the death telegrams; and the two scenes where "Sergeant Mackenzie" dominates the soundtrack as the Air Cav head for Ia Drang, and again as they make their final charge.
Someone already mentioned Shawshank Redemption- for me it was about thirty seconds earlier, when they haven't quite figured out what happened to Dufrain... The warden throws a pebble at the Raquel Welch poster, finds the tunnel,...and my heart was in my throat. Incredibly uplifting.
Blackhawk Down has a scene that is very personally moving for me, when Shugart and Gordon try to keep the mob away from Mike Durant at the second crash site.
Getting away from war movies, Interstella 5555 has two sequences that always give me goosebumps; when "Shep" gets the distress call in "Digital Love", and the montage that leads to the Crescendolls returning home during "Face to Face."
Lastly, one that speaks to me as a father- in Pet Sematary the main character sees his son about to be run over by a truck. You can see what goes through his mind as he tries to push his son out of the truck's path- he knows that that he'll die if he saves his son's life, but he's alright with that, he's made up his mind and this is what he wants to do. It's the same sort of spirit that motivated Shugart and Gordon in Mogadishu, in a way, but it's hard to understand unless you've been in that situation: I can save this person, and I'm going to try, even if it kills me.