majority of these are from sonic games (and are probably riddled with spoilers) but-
In Sonic 06, specifically Shadow's story, this line from Rouge: "Even if you believe everyone in the world will be against you...know that I'll always remain by your side" and right after they find out about how he'll be betrayed in the old future before the "Final Story". It's meaningful because it really kinda solidifies the closeness between Team Dark especially if you consider the context of Sonic Adventure 2 and Sonic Heroes.
Sonic and the Black Knight, aside from Sonic's Excalibur transformation (and some other scenes), there's this line just before where he mentions "it was never about chivalry for me, i just gotta do what i've gotta do" which in passing seems like a corny generic Sonic line but within the context of the game where he's constantly got folks reminding him of the knight's code of chivalry he makes clear that he serves no master but goes by his own will, a very signature sonic trait and the delivery before the cgi animation is honestly pretty badass. There's also this bit of dialogue after that final boss fight:
Sonic Unleashed, a personal fave game, there's like a bunch but it's specifically the exchange between Chip and Sonic after Chip regains his memories and recalls his purpose as Light Gaia; one part being where Chip explains Sonic's strength of will to not bend to the corruption of Dark Gaia and then this scene right after:
it's actually like the whole thing but it's really sweet
Sonic and the Secret Rings (I wont bother with clips) but as much as people joke about it, it was the way that rather than judging Shara at the end for nearly betraying him and almost sacrificing him to the Erazor Djinn (before offering herself instead) or the fact she would even go back to him despite him trying to destroy the world of the arabian nights he consoles her telling her she can cry as much as she needs to (the mountain of handkerchiefs bit)
Breath of the Wild, a lot of the memories between the champions but also Zelda, specifically this one:
It's mainly the part at 1:04 where she asks the what if question. It hadn't quite hit till I'd seen this comic on tumblr, but the idea that Link is essentially facing similar experiences to that of Zelda's where after 100 year slumber he's got everyone reminding him, telling him, that it's his duty to fight Gannon and to rescue Zelda. Lots of you musts and you have to and it just seemed interesting in retrospect to consider the burden's they'd shared both in the past and in the present timeline of the player's journey in BotW.
Splatoon 2, namely in the Octo Expansion where Agent 8 and Cap'n Cuttlefish are about to get put through the blender. It's the way it dawns on the player that before Agent 8 there have been thousands of deep sea dwellers and others trapped in Kamaboko's gauntlet who eventually join the dna "soup" and you're just trudging through that goop. Then on top of that the screams (a long standing bit of the Splatoon lore iceberg) that are revealed to be those among those thousands now in the goo and desperately trying to save Agent 8. The clip does it more justice but it's...a thing
Another I can think of would probably the Sans "dates" in Undertale, especially the one at MTT Motel where he talks about his encounters with Toriel at the door to the Ruins and then gives that "hang in there kid cause someone out there is rooting for you" alongside the classic "despite everything it's still you". True Lab will also never leave me and a lot of the lore that in one way or another connects to Gaster, from the True Lab entry, to San's lab behind their house in Snowdin, the mysterious grey door and all the Gaster followers (i still remember the encounter i had with goner kid in my playthrough that gave me chills). Deltarune gets some cred too with some of the ways Kris responds to the players actions but also that big heart scene at the end.
The last probably being some assorted moments in Portal 2 from Wheatley's betrayal to Glados discovering her connection to Caroline. I'm also fond of the bird scenes and the iconic lemon rant. Also curious as to the Vault scene at the end of the co-operative testing part with the two robots but much like Half Life no one really knows if we'll ever see a third game installment to elaborate on the story/plot.