Heartwarming / The Legend of Zelda: Twilight Princess
A very brief moment in Twilight Princess, during part one of the extensive final battle (battles?) at Hyrule Castle. After successfully working together to win part of the fight, Link stands holding his sword, and Midna drifts over to lean companionably against his shoulder. They grin at each other in a very "I've got your back, buddy"◊ kind of way.
Also, Colin's speech when he wakes in Link's arms after being rescued from King Bulblin is damn near heartbreaking with its youthful earnestness.
If you go into Colin's house, you can see a picture he drew on the wall of him and his family, including his then-unborn baby sister.
One from the last battle. After Link and Ganondorf's final showdown on Hyrule Field, the ancient enemy staggers to his feet to be mouthy one last time before the Triforce of Power abandons him and he finally dies (standing up no less), the camera shows the three wielders of the Triforce standing together for the last time. While Link gazes upon the defeated King of Evil, Zelda stands behind him; she bows her head and clasps her hands. What she is most likely doing is praying for the soul of her enemy.
The most indisputable example of this has to be Midna's return by literal Deus Ex Machina, and Link running full tilt to welcome her back.
More importantly, that scene was definitely a moment of Awesome, Heartwarming, and Funny all in one. For once, someone gives our Heroic Mime a reason to be speechless.
Midna's being brought from the brink of death qualifies. You can Take Your Time, but the labored breathing is surprisingly effective in creating a false sense of urgency. She gets better, but realizes what a Jerk Ass she's been.
It even shows in how she speaks, no less. After Zelda revives her, Midna speaks in a different, softer tone. It was a small detail, but a surprisingly effective one.
"Ungh... L-Link... hurry to Zelda..." How could you possibly not?
What puts it into overdrive is when you get to Zelda and realize that Midna wasn't telling you to get there fast so she could be healed. She wants you to get there so she can tell Zelda how to help you!
Also, when Zelda's soul is finally restored to her body and Midna is actually moved to tears, rendered unable to find the words to thank Zelda for what she's done for her ("Princess Zelda, I... I...")
Yeto and Yeta embracing each other when you finish the Snowpeak ruins. The simple, pure love the two yetis have for each other is touching.
"Forget mirror, Yeta... No. Look into eyes of Yeto... Look in reflection of Yeto’s eyes... There true beauty! Who need mirror?"
You get the Heart Container of the dungeon. And about 30 recovery hearts. Just from the love the two Yetis have for each other, after they reunite. How is that not a heartwarming moment?
Those two are ridiculously adorable together anytime they make an appearance. Before the end of that dungeon, all Yeto does is worry about how ill Yeta is and fix a soup to make her better (which includes catching a fish which, according to the Zoras, is very difficult to get a hold of). After, you can find the two of them hanging around on the mountain peak, all happy and ready for some fun sledding down the slopes.
What about the scene when Zelda receives the Light Arrows? She and Link stand alone in the ether, and she begs him to lend her the last of his considerable strength to save her kingdom. And bows to him — she, the Princess of Hyrule, bows to a goat-herder, in a moment of true humility and grace. Heroic Mime that he is, he doesn't get a cool line... he just gives her his hand.
The scene in the end credits, which shows Shad, Ashei, and Auru performing an archaeological exploration of the ruins of the Temple of Time. Not only do you get your proof that they survived their portion of the fighting at Hyrule Castle, but Shad — having devoted his life to trying to prove that the Oocca existed and having that aim fulfilled for him by Link — has turned his scholarly mind to ever more pursuits for the good of Hyrule. (Also, it shows him and Ashei being quite chatty. Could they be an OTP?)
When you first reach Gerudo Desert, Midna reveals the dark history of her people, the Twili. After her story, she reaches up and touches Link's cheek, asking if he's still up for this. Link just smiles.
Ilia getting her memory back. It's the cutest and most heartwarming scene in the game, especially after everything you went through to get it back, and seeing her finally recognize her childhood best friend after all this time...
The whole plot arc about Queen Rutela, which is especially heartwarming in the credits, where her spirit is seen watching over her son Ralis.
"Tell him... his mother loves him without end..."
Midna and Link get yet another one near the end. When you get the completed Fused Shadow back and Midna goes through a rather unpleasant-looking transformation, after she shatters the barrier around Hyrule Castle and the screen fades to white, we're treated to a scene of Link holding Midna, smiling, while Midna stares back into his eyes, clearly still woozy from the sudden power rush. It was this troper's favorite scene in the game.
There is the moment in Hyrule Castle when the chest containing the Boss Key is in sight, and enemies begin to run towards you. Then a hawk swoops out of nowhere, and the camera cuts to it landing on Rusl's arm. He helped you out with the hawk you taught him to use.
At the end of the game where where Colin takes up the sword and shield, and his baby sister is born. He has grown greatly from the shy child who admires you at the start but has a repulsion towards the idea of swords.
"The sword accepted you as its master..." gains a lot of weight after you've played through Skyward Sword.
It's easy to overlook, given the implied Tearjerker behind the confirmation of the Hero's Shade as the spirit of the Hero of Time, but notice how his tone shifts as he challenges Link with each new technique and watches his successor match him strike for strike. There's real pride in his words, watching the new Hero fulfill his utmost potential under his tutelage. At the end, when the Hero's Shade confesses to Link the secret of his heritage, you get the sense that Link has helped him as much in return by allowing him to absolve the regrets of his past life. Now he can finally rest in well-earned peace.
The final song Link and the Hero's Shade share together ("The Ballad of Twilight") is both an Awesome and a Heartwarming moment.
Epona is one of the few who recognizes Link as a wolf, signifying the strong bond between them. She also tells him to hurry up and get back to his normal form, which is especially poignant after Link is cursed by Zant to stay in his wolf form forever, which is the first time you can talk to her as a wolf.
Technically not a 'moment' per se, but the way Hyrule feels alive again by the time you retreived the Master Sword. There's activity everywhere—from the Zora swimming in the various rivers and lakes, to the Goron who are helping out Kakariko Village and some even going to Hyrule Castle Town, to Agitha searching for bugs just outside the gates of said city. Especially when compared to the state of things when you first left Faron Woods, when most of the land was still covered in twilight and both the Zora and Goron were desperate for help, and everyone very much kept to their own instead of venturing out.
There are even Zora in Death Mountain's hot spring area. Granted, they're not particularly used to the heat, but the fact that they're willing to go through such a hot and dry area to check it out speaks volumes.