In Volume 1/Episode 9, when Klein asks Asuna to take care of Kirito. It's played for laughs in the LN, but is heartwarming in the anime.
Chapter 19 when we finally get to see the story behind Asuna and her actions with Kirito and damn is it full of fluff from their accidental meeting and to their in-game marriage.
The last parts of Chapter 15 and up until 16 and its aww.
In Volume 2/Episode 3 "Red-nosed Reindeer", Kirito intends to solo a level boss to get a resurrection item to revive the dead Sachi, but is slipping deeper into a Death Seeker phase. Klein shows up, with the rest of his guild in tow, and begs Kirito to party with them and challenge the boss together, because Klein is afraid he'll die if he tries to solo the boss. When a PK-happy guild shows up, 30 men strong, Klein leads Furinkazan's 10 man guild to Hold the Line and give Kirito a chance to beat the boss.
After the boss is defeated, and Kirito learns the resurrection item won't work for Sachi, he gives it to Klein.
After that, during the Christmas of the first year in Sword Art Online, Sachi's recorded message for Kirito.
Agil's wife kept his cafe running, and waited patiently for him to come back to her. He did.
The entire chapter/episode focusing on Kirito helping Silica revive her pet dragon Pina is just filled to the brim with this.
In Volume 7, overlapping with Awesome: Kirito and Klein arrive to Hold the Line against a rival guild, so that the Sleeping Knights and Asuna can challenge the level boss.
In Volume 7, Ill Girl Yuuki logs into ALO one last time as she's dying, to say goodbye to her friends. And then the leaders of the main factions of ALO perform a fly-past with their members. Over ONE THOUSAND ALO players from different factions put aside their differences to give her a send off.
Beyond that about two hundred players come to her real world funeral, surprising her remaining family who thought she had no friends.
Volume 4's denouement. Kirito and Leafa dancing together in the sky, and coming to terms with their emotional baggage.
For the anime, the end of Episode 10 where Kirito asks Asuna to marry him is chock full of this, and has a very powerful When She Smiles moment.
Episode 14, where Kirito and Asuna finally tell each other their real names. And when Kirito wakes up in the hospital, weak from two years on life support, he immediately gets up to find Asuna.
Episode 24: Kirito and Yui finally reach Asuna's cage; hugs and tears all around. After Sugou's dealt with, Asuna and Kirito embrace once again; she calls him her hero and while he says he's not one, he'll try for her sake. Asuna logs out and hopes that Kirito will be the first thing she sees when she wakes up. When Yui returns, (having been banished by Sugou) she hugs her papa and then asks if her mama is okay. Even Kayaba contributes by giving Kirito a Heroic Second Wind and a I Was Just Passing Through excuse.
The last twenty or so minutes of Episode 25, so much. Kirito and Asuna finally meet in real life. Asuna's hearing is off because of her prolonged dive but she understands what Kirito is trying to say. The next scene sees them in school, eating a lunch Asuna made, then sharing in minor PDA. The screen pans out to Lizbeth and Silica with their I Want My Beloved to Be Happy. THEN there's a party for the survivors of SAO that celebrates Kirito clearing the game. Back inside Alfheim, Leafa shows Kirito how to dance inside the game and then everyone (Asuna included, who is now an Undine) flies toward the reborn Aincrad.
In Volume 9, we get this from Eugeo: "Whe-When we were young…we promised…me, Kirito…and Alice, from the day we were born together, to the time we die together…this time, I must definitely…protect…I must…"
A small but meaningful detail: In Episode 1 of the anime, there's a scene of a G.I.R.L. and a young looking man revealed to be a skinny man and a stout somewhat older man when Kayaba resets all the player avatars to reflect their true real-world selves. A few episodes later, they're seen talking together. At the end of the Aincrad arc, there's a brief scene in a hospital where these two men reunite as bros in the real world with much happiness, to the surprise of the hospital staff. Well, they didn't find love per se, but a close friendship is fine too.
Episode 23: after finding out who Kirito is, Leafa challenges him to a sword fight. In the middle of the fight, she throws a fight, but he did the same as well. Then, they hugged each other and apologize for keeping their true identities a secret from one another.
Once Kirito enters into ALO he checks his inventory to make sure a very special item is still there. When he selects it Yui appears and he embraces his daughter tightly in their first reunion since SAO.
Once the ALfeim arc is finished, the extra addition follows the SAO crew going on an underwater quest so Yui can see whales. It's very touching the lengths they're willing to go in order to give the little girl a fun experience.
Episode 7, Season 2: Kirito is telling his nurse Aki about how he killed three people in SAO and only now feels the guilt for it due to having encountered one of the survivors of the group they were part of. What follows is Aki reassuring Kirito that he did the right thing and that he deserves to move on from the guilt.