One from the first episode: Tamaki, who up until this point had seen Haruhi as the club's Butt-Monkey, helping Haruhi fish out her stuff from the pond. He's the one who finds her wallet for her, despite her protests.
This gets taken Up to Eleven in the live-action as ALL the club members band together and help find her wallet.
Episode 9: The Host Club's Straw Feminist rivals from the Zuka club are trying to lure Haruhi away and it doesn't help their chances of keeping her when it's revealed that they actually sold one of her mechanical pencils as a souvenir. After Haruhi storms out Tamaki comes up with A Simple Plan to keep her. When she shows up with the Zuka club the next day, she finds the Host Club (minus Mori) in drag, singing an improvised theme tune. As the Zuka club stare in shock, Haruhi literally laughs until she cries as she's chased around the room by crossdressing Yaoi Guys. Heartwarming for three reasons: The fact that the Host club were willing to go in drag for her, Haruhi's joy and amusement at what they did, and the fact that, naturally, she was never going to leave in the first place.
What deserves one of the top spots and which was sadly cut out of the anime (for happening around the same time Eclair was introduced), is when Haruhi during the dance meets up with Tamaki to which he asks her if he can have a taste of the food. Haruhi's reply is to nonchalantly tell him to eat off her fork, which causes the rich people in the room to stare at her in shock and whisper behind her back at her "bad manners", and even Tamaki appears to get embarrassed. Haruhi realizes this and frantically apologizes, specially when she notices that Tamaki's grandmother is watching too, when Tamaki suddenly grabs her hands with the fork and eats off it anyway, saving her from being humiliated, and calmly tells her how he's himself before he's a Suoh. The look she gives him at his action appears to be a defining moment of her falling for him.
The end of Episode 11. Nekozawa runs out under bright sunlight (which he is deathly allergic to) to "save" his little sister Kirimi from a cat. He does, but collapses to the ground shortly afterwards. Three days later, Kirimi finds him in their mansion, dressed in his usual dark attire (which she had previously been terrified of). She grabs his cloak, looks up at him, and smiles.
In Episode 8, when Haruhi leaps at Tamaki in fear, and he whispers that she doesn't have to be alone any more. Gets me every time.
After spending the entire episode trying to find what can scare her, he is very protective and tries to make her feel better. The thing that seals it, however, is that he doesn't tell anyone else in the Host Club, trying to be nice to her instead of winning the challenge.
And then there's how he saves her from drowning.
On a related note, when Tamaki finally does tell him about Haruhi's fear of thunderstorms in Episode 16 Hikaru does everything in his power to comfort Haruhi instead of teasing her. It's a massive Character Development and his first truly non-selfish act in the anime.
Episode 14, Tamaki and Haruhi are in the pavillion in the hedge maze. Tamaki tells Haruhi the story of his childhood. In the Host Club, Tamaki would have been covered in sparkles, the background changes into a carpet of roses. Instead, he's surrounded by actual climbing roses and there's not a sparkle to be seen. There couldn't be a better way to show that Tamaki really feels something for Haruhi - whether he knows it or not. The string-heavy rearrangement of the opening theme helps, of course.
From the same episode, the president of the newspaper club, Akira Komatsuzawa, is determined to portray Tamaki as an evil, manipulative creep as payback for Tamaki's club being more popular. Everyone but Tamaki and Haruhi realize this, and when they catch him in the act, Kyouya, Hikaru, Kaoru, Honey, and Mori corner him and...proceed to calmly explain what a great guy Tamaki really is, how they will not allow anything bad to happen to him, and while their family money gives them the power to destroy Akira's family, they would never do such a thing, as it goes against their principles. Yes, even Kyouya and The Twins display genuine loyalty to Tamaki, and handle the situation in a reasonable, non-malicious manner.
Volume 12 of the manga, when Kyouya, who has repeatedly stated that he only does work when it profits him somehow, tears up the French countryside to the point of exhaustion, looking for Tamaki's mother.
Later on in Chapter 78, he yells at Tamaki's father for using his own son in his plan without thinking about how Tamaki would feel about the outcome.
In the final episode, when the police force tries to stop the club from going after Tamaki Hikaru's first instinct is to get in front of Haruhi so he can protect her.
The panel that shows Haruhi getting a big blush on her face after Tamaki's kissed her forehead a second time.
Pretty much all of chapter 80, when everyone is working together to help Tamaki see his mother before she goes back to France.
And then Tamaki saying "I love you" to Haruhi at the end of chapter 81.
Near the end of the manga, Haruhi decides she needs to come clean to the rest of her classmates about being a girl. The Host Club throws a party, but Tamaki and Kyouya convince Haruhi to do things their way instead of just out and saying it, resulting in all of the club's customers getting together and telling Haruhi that they already knew, and they still support her and her relationship with Tamaki.
The last chapter then makes it hilarious and still kind of heartwarming - they didn't actually know Haruhi was a girl. They thought the "secret" was that Haruhi was a homosexual cross-dresser in love with Tamaki, and they accepted it wholeheartedly. Indications are that, while surprised by the truth, they're still not upset about it.
Chapter 83, the last chapter of the series. Where the Host Club decides to all study abroad to be with Haruhi and Tamaki.
And also the scene before it where Haruhi discovers that Tamaki was coming with her to America.
Tamaki: But I'm sorry...I have no intention of leaving you, ever. Big Damn Kiss ensues.
There's plenty of "Aww" to go around near the last half of Chapter 53, especially this:
Hikaru: Kaoru, we're twins. Isn't it an incredible gift? Normal people can only face their future alone; you and I can face it together. We aren't depending on each other. From now on, we'll influence each other; it would be good if we could stimulate each other. If we don't forget this, then, for sure, a future twice as fun as other people's awaits us! Didn't you know... that's why twins are born?
A moment exclusive to the live action drama — in Episode 5, it's revealed near the end of the episode that Kyouya also dove into the water to save Haruhi and was the most concerned for her safety.
All of Tamaki and Haruhi's interactions as a couple, especially the one-shot where Haruhi looks at a sleeping Tamaki (he fell asleep waiting for her to finish her homework so they could cuddle and watch a movie together). Her inner monologue where she expresses that Tamaki is not the only one who wants to spend time together and that she just doesn't know what to do is pretty d'awww worthy.
Not to talk about the book Tamaki was reading before he fell asleep: Married Life for Husbands. D'awwww!
Mostly based on what could have been as opposed to what is. Had Tamaki never met them, Kyouya would likely have become the cold, sociopathic type, the twins' "pranks" escalating to be far more malicious as well as them possibly never opening up to anyone, ever. Honey would be living a lie, and Mori would have to watch it happen. Haruhi would have remained her indifferent, inexperienced self never looking to expand her world or grow close to people, possibly even causing her to fail at her lawyer dream, never quite understanding why. I guess it counts as Nightmare Fuel, but it feels so nice to see what could be, but never will be now.
No mention of Episode 10 where the Host Club visits Haruhi at her home and meet her father? Granted, the episode itself is more comedic then anything else, but then there's the flashback. Ryoji is depressed because Haruhi didn't tell him about a Parent event at school, and becomes even moreso when a rather tactless co-worker of his tells him it's likely because Haruhi is embarassed that her father is a transvestite. As it turns out, Haruhi isn't the least bit bothered by that, she didn't tell him because she recognizes how hard he works for her sake and wanted him to spend his time off resting.
In the anime, the episode that explains how and why Tamaki and Kyouya became friends. Tamaki pisses off Kyouya to no end idiotically asking for things. Turns out he just wanted his friendship. D'aaaaw!
In the last chapter, Haruhi shows signs of regretting her decision of going to America, because of how much she'll miss Tamaki. Can we have yet another D'awwww?
Just the fact that the japanese seiyuus returned to voice a drama CD that involved the most important lines from chapter 80, such as Hikaru encouraging Haruhi to go and persuade Tamaki, Haruhi scolding both Tamaki and his grandmother, and her confession at the very end, among others.
It doubles as a Crowning Moment of Funny when the Host Club themselves are apparently listening to the CD, and right when it gets to Haruhi's confession, the tape stops working, causing Tamaki to cry his eyes out. After the Host Club leaves the room however, the tape starts working again so the listener gets to hear Haruhi's final line.
"Tamaki-senpai no koto ga... suki dakara."note "Tamaki-senpai... I love you."
Before brefriending Tamaki, Kyouya compared his life to painting a picture inside of a set frame. He can only do as well as he can within the permitted confinds. After embracing his friendship with Tamaki, we're shown that pretty flower picture... with colors leaving from the flower, over the frame and onto the wall creating a massive multi-colored flower. A perfect metaphor for the potential he now has.
In Chapter 71, Honey and Mori are getting ready for their graduation, causing Tamaki to get depressed. To this, Haruhi has moments of wanting to comfort him, but ends up getting interrupted each time. Towards the end of the chapter however, she comes to the music room only to find Tamaki being the only one there, sound asleep on a window shelf. After humorously inspecting him a little, she suddenly hears him say "Mommy..." in his sleep to which she finally dares to reach her hand out and caress his head. It doubles as a Tear Jerker in that not only is this taking place, Hikaru is also shown to be standing outside of the room, having witnessed Haruhi's action and wearing an expression that simply appears to say "I knew it..."
The panel of Anne Sophie's reaction as she turns around to see Tamaki tops everything...
Mei mentioning that Haruhi's pregnant in one of the post-ending extras (a few years into the future).
Plus, Hatori stating that she imagined the first Host Club member to congratulate them would be Mori.
Everything Kyouya does to find Tamaki's mother Anne Sophie while he's on the school trip to France, all while pretending he doesn't care. Squee.
The last couple of chapters seem to tug between tearjerker and this. Seeing all the people Tamaki's met trying to get him out of his house to meet his mom and Tamaki himself showing such dedication to his grandmother just warms heartstrings.
Just the scene with Tamaki at Kotoko's grave, telling her how much he loved Haruhi.
Kasanoda getting accepted by his classmates as a nice guy and getting the friendships of many girls, and even Hikaru and Kaoru.
The post-ending bonus chapter about an evening Haruhi and Tamaki spends together the 8th month in Boston. Haruhi finds Tamaki asleep on her couch after she's finished studying, and feels sorry for how little time she gets to spend with him when she badly wants to. Next thing she knows, Tamaki reveals to being awake and pulls her onto his lap, causing much flailing from her until she accidentally hits his face with a book. After frantically apologizing, Tamaki tells her that it's a book on "how to be a good husband" of which one of the points reads "remember to express your love to your wife daily". Haruhi blushes and tells him to stop reading it already, when he tilts her lips towards his and reads "remember to kiss her every day"... only to be interrupted by a sudden loud rumble from Haruhi's stomach. They blush and laugh about it and is later shown watching a movie while sitting in an adorable coupley position.
The look on Haruhi's face when Tamaki moves in to kiss her deserves a mention. She goes from flushed and embarrassed at his reading from the book to the cutest "kiss me" face.
The ending of the dream in the Alice's Adventures in Wonderland-themed episode, where Haruhi's mother, posing as the setting's Queen of Hearts, tells her that she's very proud of her. Haruhi happily jumps into her arms to hug her, and makes it before waking up again.
The twins' reasons for giving up on their feelings for Haruhi. Kaoru believes his brother needs it more and Hikaru is too loyal to both Haruhi and Tamaki to get in the way. In the exchange where this is cemented, Kaoru's horror that Hikaru might actually consider being delighted at Haruhi and Tamaki's forced separation and Hikaru's being adamant that the very notion is repugnant to him is also sweet.
Haruhi calling out Kyouya's father on his treatment of Kyouya in the last episode. She makes it clear that no one would get away with hurting her friends.
In a manga exclusive arc where the Club is trying to figure out who's trying to blackmail them into dropping out of a competition, a classmate who believes that his reputation was damaged by the Host Club throwing the previous year's competition (which they did but due to family concerns) mocks Kyouya's status as the third son of his family (implied to be motivated by Kyouya humiliating him when they were 6 due to knowing more about fruit than this classmate, heir to a massive fruit business). All of the other hosts immediately jump to Kyouya's defense; Tamaki in particular looks truly angry in a way he rarely is and even spends several pages worrying over Kyouya's well-being, which Kyouya is shown to be quite grateful for despite his stoic demeanor. Later when the Club's rival pushes Haruhi into a pool, the rest of the club freaks out and only Kyouya's insistence prevents Tamaki from throwing the contest to rescue her.
The blackmailer turns out to be a student council member who is in a Perfectly Arranged Marriage with the rival and just wants him to focus on their relationship instead of his rivalry with Kyouya.
In one of the omakes, Tamaki's first day when he moves into the second house. In his room, he laments that he isn't welcomed by the staff after a short series of events. That is, until a puppy runs into his room followed by the staff. As it turns out, they HAD been looking forward to meeting him, but the maids got nervous due to his looks. They then sing him a welcome song and tell him they were all interviewed to make sure that each staff member could give him full and loving care. And at the end, Tamaki's father is shown dressed up as a ninja to surprise his son!
Tamaki kissing Haruhi in chapter 81. He does this as a reaction to her saying she's not sure if she loves him, and tells her that whether she liked being kissed by him or not should make her know. Haruhi blushes and shyly admits she "didn't dislike it." Better yet, the shot of her reaction has a sparkly background behind her, the same background used earlier in the show when she tasted food she found really delicious. So yes, not only did she "not dislike" being kissed by him, she loved it.