I want an emotionally moving game.

if you have a ps3 try the metal gear solid series if you get connected to the characters the 4th will make you ball your eye's off

Metal Gear Solid 4: Guns of the Patriots. It's only for PS3, but it's an excellent game! Metal Gear series has best story, and it's probably the best game series ever. People who played some of MGS games knows what I am talking about. Don't listen to the people who recommending you Battlefield: Bad Company 2, DOOM 3, Metro 2033 etc... Tell me, how these games are emotionally moving???

Heavy Rain, definitely.

I Have No Mouth And I Must Scream
Papo & Yo
To The Moon
Nier

Bastion, Braid, Machinarium.

Those are all that comes off the top of my head.

A pity you don't like Mass Effect, ME2 was pretty awesome.

Max Payne 2

Deus Ex series. I have yet to play the original and IW but they're already in my Steam account.
HR will seriously move you. I dunno about the other 2, but I bet they will too.

Assassin's Creed series, cool history, cool things and other.

Earthbound

Mother 3

I heard spec ops the line makes you feel emotional at a certain part

Final Fantasy X, Skyward Sword

Try any game in the Call of Duty series. It emotionally moved my ps3 to the concrete

Metal Gear Solid, Nier, VALKYRIA CHRONICLES, Bioshock, etc.

Are you looking for PC games or PC and console?

Lost Odyssey.

Mafia.

Here's one no one said yet: Pokemon Mystery Dungeon 2: Explorers of Sky.

It's got some pretty dark theme going on despite the cute design and a lot of shit getting past the radar.

Advanced Kitten Shooter 2012?

Thirty Flights of Loving :D

Shenmue. That's the game you're looking for.

Sonic The Hedgehog 4

You already named it yourself: Zelda
PC games can not touch Nintendo's art.

Mario Kart: Wii

Street Cleaning Simulator is pretty emotional for me..

R.I.P Steve, I'll never forget you. :'(

Bastion, The Void, Deus Ex: Human Revolution, Trauma, Scratches: Director's Cut (one of two games to ever make me scared for my life), Fallout 1. That's all I can name off the top of my head, none are tearjerkers, but all evoke emotions you did not know you had

I'm 34, The only game that has managed to move me to tears was Final Fantasy IX
The ending scene & music was just too much
If you don't mind emulating I suggest giving it a try.