Several...
<spoiler=Asura's Wrath, Episode 12 - Gods of Death> Skip to 9:48.
This game is like playing a high quality anime TV show, and all of it's moments are heart gripping. Not only do i care about the main characters, I also care about what the villains are up to. You get this game for dirt cheap now, so it's worth it.
I've said before, and I said it again, most of the classic DMC games knew how to strike a balance between humor and seriousness; and DMC 3 knows how to do it. It does it the best out in the series. The DmC Reboot failed in every aspect in terms of story, writing, dialougem character development, and most importantly, gameplay.
<spoiler=Streets of Rage Endings>
These brawlers may not have much story, but I still care more for what happens those games, than I do for most AAA games with "cinematic" stories. The good endings make me feel like I accomplished something and the bad endings feels like "Oh my God, what have I done?/I screwed up!". The first time I got the bad ending in SOR1, I felt like shit at the age of 4.
Confusion and sadness. One you know that the Killer 7 never existed, and Garcian Smith (Emir Parkriner) was just a man with split personalities, it's all heartbreaking. When he learns the truth, you can't but feel bad for the assassin. I actually teared up a bit; the music set the mood perfectly.
<spoiler=No More Heroes 2 - Alice Twilight> Skip to 1:44.
I will never forget you, Alice.