Ayane's ending in Dead or Alive 3. Yeah, lot of converts to team purple here, so to speak. Because sometimes...ninjas cry too.
Her entire backstory is a Tearjerker. She and Kasumi are Childhood Friends and sisters...and because of the various ninja politics and the misfortune of her birth, Ayane winds up separated from the only friend she ever had, only to come back when she's assigned to kill Kasumi. And then she has to kill her adoptive father after he's made into a monster? Ayane, a Woobie is you. And then they set it to Dream On. That opening sold me more on the series' storyline than anything in the actual game.
For non-ninja characters, Helena's ending DOA 4 is a fairly tear-jerking summary of her entire story to date, as she decides to atone for the pain that DOATEC has caused everyone by blowing it and herself up with the self destruct. The Aerosmith ballad playing in the background just adds extra punctuation, along with Helena's melancholy "Sayonara...". But then Zack swoops in for theDynamic Entrysave, so it's alllll riiiight!
I'll also put in Jann Lee's DOA 4 ending where it shows that he's more than your average Arrogant Jeet Kune Do Guy. Turns out he's piss poor and the locals seem to enjoy bullying him for being a weak kid, and take delight in tormenting him like offering him a meat bun when he's hungry, then tossing them to the ground, beat Jann up while laughing at him and stomp on the food right on his face. It was so bad that his only escape in the harsh reality is watching Bruce Lee movies, even in not-so-luxurious state. It's true that it was because of that he is inspired and became strong, but still, damn that's some sad childhood, and it's just thanks to Bruce's influence that Jann could get out of that hellhole...
Hitomi seemed really broken up when she discovered Ein wasn't his actual identity. By DoA5 she seems better (though she tends to forget that "Ein" isn't his real name) but when she first gets the news it hits her pretty hard.
False Kasumi's death in DOA5. Putting aside that she was Actually a Doombot, the poor thing still had all of Kasumi's memories and was fully capable of feeling pain and emotions. To Ayane and Hayate, they were just putting down an imitation of their former ally, but from the clone's perspective she was murdered by two of her kin who she once loved and trusted.