It is interesting to see how many of those games that hit us emotionally were developed by Asian countries. The games that hit me emotionally that are obvious include:
Final Fantasy X
When I beat this game, my brother had gone to college. I could relate so much that I actually cried, not just teary eyed; when this game was beaten I was in tears. My parents were dumbfounded until I explained it 30 minutes later. It is plain and simple, missing something you cherished and something you wanted to stay with, but they make it so dramatic and so sad that I couldn't hold back. This game was just one of those games that forever will hit everybody, because everybody loses something they cherish.
World of Warcraft
To date there have been countless "studies" on how this game affects us emotionally, mentally, physically et cetera. World of Warcraft was by far one of the most powering games because you felt like you could accomplish anything. When my guild downed Ragnaros for the first time, we thought we were the best players in the entire world. It wasn't until mid-way through BWL did Elitist Jerks / Goon Squad start up their theory crafting fame. This was a game that not only was very satisfying when doing something like a raid, but even when farming materials to sell or use, you were like "Yeah, I would devote my time to this." I still regret not continuing to play, but then I look at how much fun I am having now without the game. While it was a fun game, it was to much of a time dump that was too much fun. I cant replace the friends I have now with in-game friends, how could I ever depend on them for real situations?
Call of Duty
The original was probably the most touching war game I have played in a long time. How many times does a game actually feel like it is tailored to honor those veterans that have fallen for its citizens? Not many, most of the games put out are your generic run-and-gun that have little meaning to what they actually do. This dislinkage nowadays can be seen all over gaming blogs and getting flames from the readers and praises from the mothers.
Call of Duty 1 was different, this game hit on what it meant to be a soldier. You had to put up with the crap, do things that tested you limits all the time. If you ever watched Band of Brothers, probably one of the best HBO series, you could follow it and get even more out of the game. The scene where Lt. Spears mows down the PoW's, was just a scene in between say Carentan and Brecourt. This game could go side by side with that film, this game was ahead of its time, if it had come out now with graphics games have nowadays, it could be the next Saving Private Ryan of video games.
Now to the less Obvious
This game was the first and foremost game to really scare the #%$* out of me. Doom 3 before had taken the dark image with the "jumpy" scaring mechanics. F.E.A.R. fell into those traps very little and they really created a game that was truly scary because of how they managed the paranormal scenes. When the hallway all of a sudden closes and a girl is walking at you with the blood running up the walls and you have to run to the door to open it and FOOM, it was just a physche out. As simple as that sounds, and from a Stephen King novel, they did a good job of making it different; making this game into a movie that was actually being played. F.E.A.R. also had the most terrifying ending sequence, that was not jumpy. I remember running down the halls escaping from the science room, my brother is behind me laughing his butt off, I'm sweating balls and saying "Oh &*#^" in a squeeky high voice, and I am blowing away these paranormal bastards.
This game truly deserves the "Skid Marks in my Pants" award, this game hit on "What truly scares people."
I'm amazed to have not seen this yet; this is a game based on decisions, planning, and learning the backstories of every character and how they weave their story into the plot. Atlus has always done a fantastic job of making the characters in these games somewhat plausible and relate-able. While the plots make the heroes seem like the unsung heroes that save the world in the background, the game is based around emotional decisions of these characters.
I remember during Persona 4, when one of the characters I really liked (hint: Heaven Level), I verbally said "Oh #*&% you!" at my TV. The last time I remember saying that to my TV, I was mad at my brother for unplugging my N64 controller while playing GoldenEye (yeah I screen peaked). These games are one of those unsung games, shame more people don't play it, when you get over the anime graphics, these games are just through the room amazing.
First game I ever felt creeped out, laughed, and cried, ALL AT THE SAME TIME. This game was really crappy, really funny (if you get japanese humour), and made me sad. This game was about singing maidens and it was awesome, nuff said, this game is about music and how it relates to a fantasy world. How more awesome and random can that get? The game was easy, you laughed along the way, and got too hear some of the best battle music in a long time.
Edit: @Gamerdude: I found Crisis Core to be just a beautiful game, the plot wasn't overly complex and it just well... fit. Everything they did in that game was correct, music, tone, voice acting, they did a stupendous job. Although I didn't get teary eyed, it was probably one of the best games. What made it emotional wasn;t how it was made, its because it was nostalgic in my opinion.
@KingdomHeartsLovers: I've never played this game because I was never a fan of mixing to many random series (Disney + FF + Original Characters), that is just to broad of a spectrum to choose from, how do these characters play into a much larger role? I just don't see an emotional impact, did something happen to Sora? I feel very left out, and I'm assuming the franchise characters help him through it?