Fate/stay night had a ton of these in the final few episodes, especially 20 and 21. Just to name a few:
Rin laughing "Haha, you're so stupidly honest!! Just like Saber" at his dating-plan, then wishing him good luck, warmly stating "but that's what's so endearing about the two of you; I love you both so much.".
Ilya: "Hai hai hai! Ilya wants to meet in secret with Shirou too!"
Shirou about to take Saber's hand in the theatre when she starts imitating the onscreen swordplay, reminding him she's kind of scary.
The argument on the bridge, where Shirou tries so hard to convince Saber she deserves to allow herself a second chance, and she just won't give an inch. When he comes looking for her hours later, she's still standing on the bridge, lost in the emotions she refuses to admit she's feeling. Shirou half-pulls her back to his house where it's warm... and after a while, she steps closer to him. When she's been guarding herself so carefully, that smile they both have, and the way Saber takes Shirou's hand tighter when Gilgamesh shows up, speaks volumes.
Saber's attempt to cook for Shirou. * WHAM WHAM WHAM*
Saber wistfully sitting on the porch, wondering if she'll be able to read Shirou's future in the stars when night falls — then scolding herself for acting like a lovestruck fairy-tale maiden.
Saber refusing Kotomine's offer to join him and finally admitting the truth: she'd rather have Shirou than anything the Holy Grail can give her.
Saber's simple faith in the face of Gil's taunting: "This was the right choice. I will not lose to a person like you. Shirou will not lose to a person like Kotomine."
Most of all, the post-date fight with Gil. Shirou, barely able to stand, screams to Saber that "There is not one thing I can replace you with in my heart!" What Saber tells him when it's all over: "I finally realized it. All this time... you were my scabbard." (The fact that this turns out to be literally true only hurts the moment a little.)
The flashback to Saber's death showing Bedivere's desperate attempts to keep her from dying.
Earlier, in the Fate route Ilya has been a major antagonist for most of the route. She's nearly killed Shirou, Saber, and Rin more than once, and kidnapped Shirou with intent to make him her 'doll'. Yikes. Yet after her servant is defeated, reducing her more or less to a terrified child, Shirou, who has more reason than anybody to never forgive her past actions... picks her up and carries her home to take care of her, so she won't have to be all alone and defenseless. He never even asks for anything in return. Awwwwww.
That leads into another one. While it's most apparent retroactively after Unlimited Blade Works, hearing Ilya insist that with Berserker dead, she has no desire to keep fighting (specifically, she has no desire to stick around and find another servant; Berserker was too important to her) is a first hint that maybe she's not as psychotically evil as she seemed...
Then there's the scene the night before the battle in Unlimited Blade Works. Rin had been acting weird earlier, so Shirou goes to see her. He finds out that Rin was acting weird because the quickest and simplest way for Shirou to access the amount of magical energy he needs to use his Reality Marble is to "connect" to Rin. Shirou reacts the way you'd expect a 17-year-old with repressed sexual feelings would act, which Rin takes the wrong way and becomes visibly sad. Shirou then tells Rin that having sex with Rin is like a dream come true, but he wanted it to happen naturally in the course of a relationship, as an expression for their mutual love. Shirou then expects to be slapped...only for Rin to kiss him.
Archer's smile at the end of UBW. Just like when Kiritsugu pulled Shirou out of the fire ten years prior to the story, it makes you feel like Archer might have found his own salvation in saving Rin and Shirou, and the events of the route generally, after a long existence of pain, betrayal, and bloodshed.
Archer:"I found my answer. Don't worry Tohsaka, I'll do my best from now on too."
If that wasn't heartwarming enough, consider the fact that if you have the voice acting for that scene available in some way, you'll notice that when he says that, his speaking manner has changed back to the way they used to be. If you can tell the difference, its all the more apparent that Archer is freed, the cold, spiteful demeanor is gone, and he has become Emiya Shirou once again.
The scene in the Fate route where Saber (who has been cold and distrustful towards Illya) wipes her face at breakfast and tells her "Your hair is beautiful. It pains me to see it get dirty." Shirou thinks to himself that Saber sounds like she is remembering someone else and not thinking of Illya anymore. This scene is much more powerful if you have read/seen Fate/Zero and you realize that Saber is reminded of Irisviel.
The Last Episode of Fate/stay night Realta Nua. The idea that Saber will always, throughout time, for eternity, wait for Shirou, and that Shirou will always be trying to move towards Saber, to find her again is one of the most affecting parts of writing in Type-Moon's long history.
The clincher? They do end up finding each other. Saber has to wait for Shirou. Shirou has to endlessly pursue Saber. Shirou ends up going through similar hardships that Archer had to go through. Saber had to give up her right to be human to become King, and was met with this choice with betrayal. Up until their final moments, neither of them are how the other remembers them. When they finally meet up, Shirou can finally let go of his hardships, and Saber can finally become a human being again. When the tears she held back start falling,She wasn't the only one crying.
A minor one in Unlimited Blade Works: After Saber makes a contract with Rin, having her contract with Shirou forcibly removed by Caster, Archer points out that now she "truly has no connection with Shirou anymore", questioning her reason for protecting Shirou against him. Saber's reply? "I believe I told you, Archer. My oath with Shirou will not go away." It's subtle, but it proves Saber's absolute devotion and protectiveness towards Shirou and her insistence on staying loyal— despite the circumstances mentioned above, as well as the fact that this isn't even her route and that she isn't the love interest, and it's what makes this a CMOH.
Although it's small, this conversation between Shirou and Saber in Unlimited Blade Works:
Shirou: (About Kiritsugu) He was a troublesome adult. He was usually spaced out and clumsy. He said he's going to enjoy what he likes, and he would play around like a child. You usually couldn't believe him when he called himself a sorcerer.
I can tell that I'm smiling as I tell the story. About my past. The five years between the time of the fire and Kiritsugu's death. Come to think of it, that might have been the best time of my life.
Saber: (smiling) I see. So you liked him for who he was.
Shirou: …Yeah. Tohsaka might get angry if she hears it, but I admired him. He was free and not like a magus at all, but he was a true sorcerer to me.
Early in Fate, after Saber notices one of the stuffed animals that Taiga had brought for Shirou, she takes the lion plush, and reminisces about how she once took care of a lion cub for a month, lamenting that she could not be with it longer. And, to boot, Shirou receives the utterly adorable memory of Saber holding the cub in her arms and smiling.
The Sunny Day ending in UBW.
Shirou's had a rough day; he's found out that Sakura, the route's love-interest and his childhood friend, has been put through hell by her grandfather and raped multiple times as part of her training. To make things worse, she's also a Master in the Holy Grail War and has trouble controlling her incredibly dangerous magic. After she knocks herself out after inadvertently attacking Shirou, he goes off by himself to a park where he reflects on this new information and starts getting enraged at Zouken, as well as himself for not noticing any of this sooner. Suddenly, Ilya, the child Master of Berserker, shows up and wants to play with him. In a fit of rage, he pushes her away and immediately regrets it, knowing that he just "pushed aside an honest, pure show of affection." He can't even meet her gaze, and a Dead End seems imminent, when Ilya, in a show of compassion, apologizes to Shirou.
Shirou: .....Ilya. Aren't you going to get mad?
Ilya: No. You're about to cry, Shirou. I don't know what happened, but it'd be too bad for you if I hate you. So I'll be your ally no matter what you do.
Shirou (thinking): My vision is covered in white. ...It's just one phrase. But that phrase washes away everything from my head.
Ilya's response is really sweet considering that at the beginning she would have killed him or kept him alive as only a head for attempting to drive her away. Right now Shirou is at his lowest point in this route and perhaps the whole game. His servant Saber is gone, taken by the Shadow, his love interest Sakura runs the risk of killing many people and is currently at odds with Rin who'd been his ally in this route and other routes over whether or not to kill her. Add to the fact that he lacks the Projection and fighting techniques he had in Fate and UBW making him almost powerless. However, Ilya's  speech manages to lift Shirou's spirits up when he hears that he still has an ally. Really, most of Shirou's and Ilya's interactions in Heaven's Feel could count.
This can create a What the Hell, Hero? moment if Shirou chooses to stick with his ideals, producing the infamous "Heart of Steel" bad ending, in which Shirou is supposed to kill everyone involved in the Grail War, including Ilya.
Almost immediately following this scene (if you choose to protect Sakura), Sakura runs away on hearing Shirou and Rin discuss killing her. Shirou leaves the church, and runs around the city, in a race to find Sakura before Rin (who still intends to kill her) does. Eventually, he finds her standing on the bridge, in the pouring rain, unsure of where to go. He tells her to return home with him, but Sakura, full of self-loathing, says that he should keep away from her, that she can't go back to his house after what she's done, that she is selfish and cowardly and that she never felt she deserved she should be with him. His response? He hugs her, telling that he will always protect her, no matter what, and he walks her home, hand in hand.
On a similar note, the (in)famous But Thou Mustmoment◊. Some people seem annoyed by it, but rather than creating another bad end which forces you to pick a certain choice as the game clearly does in other instances, the idea of being absolutely unwilling to abandon Ilya is so strong that Shirou literally has no other option is touching.
Let's face it, Ilya is just one gigantic unending CMOH in Heaven's Feel.
Heaven's Feel, Day 11's lunch. Shirou sets up what looks like a clumsy effort bound to only worsen the awkward tension between Rin and Sakura. However, the result when Sakura first calls Rin "Nee-san" face-to-face is a very heartwarming (and faceburning) moment.
The end of Heaven's Feel also provides one. Rin and Dark Sakura are fighting in the cavern. Sakura makes an impassioned speech pleading for sympathy from her sister, which Rin responds to by telling her that she neither understands Sakura's plight, nor cares about it, pushing Sakura totally over the edge (and, in one bad end, where she wins the battle, over the Moral Event Horizon as well). Rin decides she can not defend against Sakura's attacks for much longer, and has to finish the battle now. Having destroyed her weapon in order to wipe out Sakura's shadows, she closes in for the kill, intending to put a dagger through her sister's heart. But, on reaching her, she realises (finally) that she does care about Sakura, and cannot bring herself to kill her. Instead, she hugs Sakura (complete with extremely heartwarming CG), and proceeds to explain to Sakura, whilst bleeding from a knife wound to the stomach (inflicted, in panic, by Sakura), that she had always loved her, had always looked out for her and had hoped that Sakura was living a happy life as she suffered the (self-inflicted) harshness of training as a magus.invoked
The True End Epilogue - Sakura and Shirou, who had to take a few months off school, graduated together. Rider manages to stay with them and having a peaceful time there, Rin at the end asks her younger sister if she is happy to which she replies with a sincere yes with the smile that Sakura gives. Seeing all of that makes Rin contemplate that her trip from halfway around the world was completely worthwhile.
The final image shows Rider,Sakura,Rin,and Shirou. All on their way to see the cherry blossoms.
The fact that in the manga, Sakura's past and Shinji are not as horrible as in the game. There is no rape, no Zouken and in the end Shinji ends regretting his actions, does a Heel-Face Turn and regains his position in the archery club and, maybe, even Mitsuzuri's friendship. Most heartwarming is to see him and Sakura getting along nicely after he loses the Grail War. Considering that one is designated as a JerkassChew Toy and the other as a Broken Bird in the visual novel, it is refreshing to see a reality where they escape the worse of those fates.