The Tokimeki Memorial series is renowned for being at the far end of the idealistic side of the Sliding Scale of Idealism Versus Cynicism, and thus for running with sweet and heartwarming romance: as such, expect to see a lot of heartwarming moments in that franchise. Here's a list of those:
Tokimeki Memorial franchise in general
Basically every Happy Ending that doesn't fall in Crowning Moment of Funny is this. Especially if Tears of Joy from the character who got her/his feelings reciprocated by the protagonist are involved, as in the case of Shiori and Nozomi in 1, Saki and Ayako in Tabidachi no Uta, Hikari and Kaedeko in 2, and Maki, Yuu and Itsuki in 4.
Also, nearly every character in Tokimeki Status during Valentine's Day.
From the Girl's Side series, any time a girl in Rival Mode gives up her guy to you and asks to be friends again. Considering that you're probably only getting this scene by going well out of your way to be her friend even though your relationship has gone back down to 0, it's a wonderful feeling to finally be friends again, especially if you were very good friends when rival mode kicked in and destroyed your relationship.
Tokimeki Memorial 1
Shiori and the protagonist's Double Birthday Event, where they reminisce on the toy ship he offered to her in their childhood days.
Saki's "Tears of Joy" Event, when she cries of happiness after you and the base-ball team she's the manager of wins the Koshien. The scene is particulary memorable, as the game uses a special crying sprite for Saki not reused anywhere else in the game.
Saki's Sick Episode special event, where she falls ill during the 3rd day of the School Trip, and you stay at her bedside during the 4th day. The sweet music box BGM and Saki's "If only I could be ill like this more often..." line she unconsciously slips out make the scene even more adorable.
Mira's Christmas Party event, where she shivers from the cold and the protagonist offers her his coat. She takes her arm to "give some warmth", and then a few days later, she gives him back the coat, with all the little tears sewn off, courtesy of her. Considering she is the Lovable Alpha Bitch of the game, seeing her being so close to the protagonist is an adorable view to hold.
Likewise, discovering Mira being so kind, caring, and adorable to her little brothers (such as in the main game, in drama tracks like her monologue in Volume 2 of Nijiiro no Seishun Forever, and the OVA), and little kids in general (as shown in Tabidachi no Uta) really adds a lot to her character.
The ending of the Shiori Route in Tabidachi no Uta doubles as Crowning Moment Of Awesome, as the protagonist, out of love for Shiori, symbolically completes the marathon route he couldn't participate in the day before due to a severe muscle tear in the leg, suffering hell in the process. Shiori, having guessed his intentions, waits for him at the finishing line all while cheering for him; and after, they confess their feelings in each other's arms. AWWWWWWWWW.
The final line of Nijiiro no Seishun 's Perfect Ending, which doubles as a Title Drop for the game's Leitmotif, as Saki and the protagonist are happily holding in each other's arms, under a rainbow: "Anata ni deaete yokatta" (= I'm so glad I've met you).
Tokimeki Memorial 2
The Blooming Stories Drama CD series are living and breathing this. Each CD has 3 Drama Tracks, placed in a order such as their contents show the evolution of the girl's feelings towards the protagonist: the first track takes place at the beginning of their relationship; the second track is when the girl has fallen in love with the protagonist; and the third track is after she has confessed her feelings to him. The heartwarming contents varies with the girls, with for example Mei having a Sand in My EyesOnion Tears scene, or Kaori gradually believing back in The Power Of Trust.
As a whole, the "Futari Dake no X-Mas" (A Christmas for just the two of us) special events for each girl are made of heartwarming, meant to show how much the two characters have fallen in love with each other. It's a different kind of heartwarming scene depending on the girl ( a Snowed-In situation for Hikari, a You Must Be Cold scene for Kaori, a Train-Station Goodbye for Kaedeko, or a She Cleans Up Nicely scene for Homura for example), but they'll make you go awwwwww.
Protagonist: Yae-san, it's fine if you bloom at your pace.
Kaori: ...Thank you. My decision is made. ... I'll enter the Volley-ball Club!
(Outside the park)
Kaori: Thank you for today. At last, I've...
Protagonist: The real battle begins now, Yae-san.
Kaori: Yes, you're right.
Protagonist: Well then, shall we go home ? I'll take you back home.
The Sick Episode event, where Kaori visits the protagonist at his home when he's ill, and lovingly feeds him with mikan (tangerine) lumps she prepared for him;
The 3rd Year School Festival Event, where, if you choose to do a Tea Shop attraction, she'll cheerfully and happily act as the shop's waitress, donning a maid costume. And then there's the camp fire scene just after...
Kaori: How beautiful...
Kaori: Thank you...
Protagonist: Eh, about what?
Kaori: If I was able to be with everyone and have fun with them like this during this School Festival, it's thanks to you.
Protagonist: ? What do you mean by this?
Kaori: No no, it's all right, if you don't understand. For now, I just...
Kaori: I just want to be like this a little more, and silently gaze at the flames... Together with you.
And then there's the Epilogue of the novel she's the heroine of, Anata o Shinjiteru, and more specifically its very last lines: see the Quotes section of the He's Back page for their English-translated version. The heartwarming is absolutely overflowing when finishing the novel on those lines.
Kaedeko's Event where she and the protagonist meet again at Hokkaido, during the latter's School Trip. The two of them feared to never meet again after Kaedeko and her family's sudden moving away from Hibikino, so the scene is very powerful and poignant.
Mei, being a cute Tsundere, has a good share of adorable Events. Among them are:
"First Food", where the sheltered girl discovers for the first time fast-food, invited by the protagonist;
"You are my only slave", showing her Clingy Jealous Girl side (and embarrassing herself in front of everyone with this);
and "Mei's memories", occuring if the protagonist met her in Childhood Mode: seeing her cry as they discovered they actually were the kids who played together back then, and renewing their promise of being together is really moving.