This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Batman: Arkham Asylum
The sequence in Batman: Arkham Asylum where under the influence of the Scarecrow's fear toxin, you relive the death of Bruce Wayne's parents. Including a point where you turn into Bruce Wayne as a child and stumble past the corpses of your parents. Eight-year-old Bruce overhears a police officer that is a dick: ("Oh, he'll be fine. Kid like that, with all that money? Yeah, I'm sure he'll be just fine... His butler's coming to pick him up... Hear that? He's got a butler.") Comissioner Gordon's the only one who takes pity on Bruce, which makes it all the more heartwarming.
The worst part is towards the end, when we hear the mugger (with a darkly distorted voice) gun down Martha. Bruce screams, the gun fires, and Batman staggers. He makes it to his parents' corpses and falls to his knees, and after a brief flash of light, he turns into his eight-year-old self. After a few moments, the Bat-signal shines down on the whole scene.
"Why did he do it, officer? Why?"
In a minor way, seeing Harley sobbing in her cell after Batman has subdued her kind of reminds you that for all her slavish devotion to the Joker, she's ultimately just a broken woman and another of Joker's victims.
Until you look at her in Detective Mode and realize she's faking it (and looking up at you every so often to see if you're buying it)... She's even laid a trap for you, and she WILL gloat.
Your first encounter with enemies with guns. An officer says "Please, I've got a wife and kids..." "You don't have to do this!" After killing the officer, the goon says "You're right, I don't have to. I just want to!"
Seeing the dozens upon dozens of corpses of innocent guards and doctors throughout the game. Easily a hundred good men and women dead.
Fridge Horror and/or Fridge Brilliance is invoked once you recall this conversation from the intro sequence where you escort Joker through the asylum.
Security Officer: So, you're back. You killed three of my crew when you busted outta here.
Joker: Only three? I'll be sure to try harder next time. What say we aim for a hundred?
Both this and Nightmare Fuel. Seeing Bruce's parents after hearing them.
The cracks in Batman's voice only make this all the more depressing.
Same as above, both this and horror. While saving Dr. Young from Zsasz, she's crying with her whole heart out, even with smeared make up. After the bomb blows out on her face, her body, left on the floor, with no one attending or taking it... just left there, all burned out and charred and bloodied. It'll be normal if she just disappears, like in any other game, but in this one, just the unconscious disappear, and because they left after waking up. But the dead stay there, even if they're cops or doctors or whatever other citizen.
Doctor Young's death in general is pretty damn sad, as she was in the middle of atoning for invertingly helping the joker make the Titan formula.
Plus the game heavily implies she had a girlfriend or wife, which means she be leaving a loved one behind.
The first Scarecrow sequence has Batman entering the lower levels of medical seeing several people freak out, including one of the feral patients that Joker will release later on. This patient is screaming a plea for help before dying from fright. Arkham City reveals that Strange experimented on these inmates to develop the mind control techniques he used on Mayor Sharp and his Tyger guards. That patient you see? He became sane enough for one last coherent thought, but only of sheer terror.
Most of the Joker interviews are disturbing, but the third one is just sad. After the Joker plays the Multiple-Choice Past card, Dr. Young tells him to focus on his real past. His response is one of the few times there's no manipulation or mockery in his voice: "What if... what if I'm too scared to remember? It hurts too much." It's still possible that he's just ballsing around again, but it's also possible that it's only just now he's finding out about the Titan Project - so maybe for once he is telling the truth?
Taken even further in the Emperor Joker adaptation, from the Batman: The Brave and the Bold animated series. It reveals that "Being sane and normal" is one of Joker's worst fears. So in a sense, these "Rehabilitation sessions" terrify him more than we would assume.
So much happens in the Warden's office that you may miss this, but there's a plaque on the wall near his safe that has a dedication on it. "May this secret be as an oasis in a desert of insanity. —Daddy." It's not made clear who put this there, the Warden or Amadaeus, but it serves a sobering reminder that, for all their flaws, they've suffered through just as much loss as Batman has.
As you leave the Medical Facility, you run into one of the distinct guards William North, you get a tearjerker laced with a sort of mournful heartwarming. After he tells you about the death of his fellow guards (which you heard earlier thanks to the Joker) he goes to one of the bodies, which he dragged in with him when he took cover and says:
Officer North: "Don't worry, I'll take care of Maria"