The cutscene that plays after defeating the Emperor in LEGO Star Wars II. Nearly every other scene is played for laughs, but the death of Anakin and Luke's final goodbye to him are played heart-breakingly straight.
Gandalf the Grey, Boromir, Théoden...each major character death in Lord of the Rings is played very faithfully to its movie counterpart (complete with dialogue from the films), and they're all heartbreaking as a result.
All except one - when you play through Helm's Deep, you'll see Haldir duelling an Uruk-hai atop the wall. No matter how quickly you climb up there, the orc will kill the elf. Haldir doesn't have a cutscene, dialogue, or anything - he just dies during the level and there's no way to save him. What a Player Punch.
The fight with Mastermind, in the Statue of Liberty. He takes control of player characters one by one, with a screen in the background showing what he's forcing into their heads. While relatively angst-free Mr. Fantastic just sees himself fighting off a bunch of Skrulls, Wolverine gets to relive the Weapon X experiment, and the Hulk gets to relive his birth as a giant green rage monster.
Wolverine: No! You can't turn me into a monster! I won't let ya!
The end of "Breaking Bats" where Batman is being controlled by Brainiac. He grabs Robin by the neck and holds him over a drop.
Robin: Batman, wait! We're a team! PLEASE! I'm your friend!
A subtle one during the visit to the Indigo Tribe, when you come across a statue of Abin Sur. It's never explained in game why this is the case, but comics fans will know that it's because Indigo-1 killed his daughter.
The climax of LEGO Batman 3 has Batman nearly being crushed by a Brainwashed and Crazy Superman. Fortunately, he's able to stop it from happening.