Many already mentioned here that had a big emotional impact on me, such as The Passion of the Christ and We Were Soldiers.
Another one, for me, is Super 8. One of the movie's primary themes is loss of a parent (the mom), and I had lost my own mom within a year of that movie's release.
One of those movies the Georgia-based church puts out (did movies like Facing the Giants), featured a man who's daughter dies in a tragic car accident, can't recall the title of the movie, but in all the stuff in the movie where he was imagining dancing with his daughter at her wedding that would now never happen, and with me being a dad to a young daughter, that got me.
American Sniper - that movie did such a great job of just putting me into Kyle's life as a Navy SEAL, as a man, husband and father, that when the ending started and we get that first glimpse of him meeting the veteran who ultimately would kill him, we see the shot of his wife looking one last time on him through the door, that I had completely forgotten that the movie was not fiction - and then it cuts to real footage of the motorcade through Dallas. That was an emotional gut punch.
Not movies, but football - I've only lost it emotionally at two football games, the first time at the conclusion of the '99 sip game after Gamble recovered that fumble and lifted his arms toward Heaven. The last was the 7-OT game against the swamp kitties. I had lost my dad earlier that year. He and I had been going to 1-2 games together each season, and for that season, we had decided to go to that game. My first couple of times in Kyle Field that season without my dad was tough, but that last game (last game I've actually attended), I literally felt my dad's presence with my wife and I, and when Rogers caught that decisive 2-pt conversion pass, I lost it.