Superman: The death of Lois Lane and Superman's reaction is both tearjerking and chilling.
Jonathan Kent's death. When he has his heart attack, he mutters, "Oh, no. Not now." It also teaches Clark that no matter how many powers he has, he can't save everyone.
On a related note, Christopher Reeve's death as well. Considering this movie was to him as Adam West is to Batman, this troper occasionally cries when he hears the John Williams Superman theme.
The scene where Jor-El, Lara and all other Kryptonians dies as Krypton tears itself apart. The film provides one of the more gruesome versions of the plants destruction.
One of the most heartwrenching versions is possibly the one shown in the 90's animated series. It includes a scene with Kara's father, one of the most outspoken skeptics against Jor-El's theory, which is implied to be heavily influenced by his dislike for his son in law. Leaving the house, he sees the rocket carrying baby Kal-El leave the planet, just as another earthquake begins, which finally hammers home to the old man that Jor-El was right.
Bystander: Another earthquake?
Zor-El: No... the last one.
The Death of Superman: The entire ending of the fight between Supes and Doomsday, where you suddenly realize that the Man of Steel knows that he might not survive this, and still keeps on fighting. Then when they both drop dead, you're subjected to 4 straight pages (2 of them double spreads) of every person whose seen the fight starts breaking out into tears. Anyone who read the comic did too. And the flag made from Superman's torn cape was just extra incentive for the water works.
The Funeral For a Friend arc that came afterwards was even worse, all starting with this: Superman Armbands.
Bibbo Bibbowski, a big-hearted lug who initially liked Superman because he was "tough", first tries to help Professor Hamilton try to save Superman (even though the only thing protecting Bibbo from getting fried himself was a personal forcefield), and after the funeral prays to God and asks Him why He would take a hero like Superman instead of "an ol' roughneck" like him.
The moment you realize that the greatest hero since the creation of modern comics has just DIED tends to make more than a few tears well up in your eyes, ending a decades long career spent saving the lives of sentient beings around the universe countless times. To quote an AC/DC song "For those about to Rock, We salute you". We love you, ya Big Blue Boy Scout.
In real life one of the entertainment news outlets that covered the Death of Superman story-line was literally titled: "Superman Falls Victim To Age of Anti-Heroes." That's incredibly sad when you remember that the 90s era of comics were being overrun with Darkerand Edgier anti-heroes, almost symbolizing that there was no place left in comics for Nice Guy heroes like Superman.
The ending of the War Of The Supermen storyline. New Krypton is destroyed. Flamebird (Thara Ak-Var) sacrifices herself to reignite the sun while Chris Kent is held back from saving her by the Nightwing entity. Chris Kent seals himself into the Phantom Zone to make sure General Zod doesn't escape, bidding a final farewell to Superman, his true dad. Sam Lane is hailed as a hero instead of the racist bastard he truly is, while everyone thinks all Kryptonians are evil.
Action Comics #800 is a retelling of Clark Kent's life from the moment the Kents found him until the instant he decides to be Superman. While that story is good (and has a few tearjerker moments itself), it's interspersed with short b+w vignettes of people in the DC Universe who have been inspired by Superman in different ways, such as the man who willed himself to learn to read because he wanted to know what Superman was saying in a comicstrip, or the boy dying of cancer who reassures his father that he'll be fine because they're "going to get all the Kryptonite out." It's the final piece that really turns on the waterworks, though: it's the story of a policeman who wears a Superman shirt under his uniform; he'd been doing it for six years, ever since another cop had been shot, and all the guys he worked with made fun of him for being superstitious. Then one day, he runs to help a woman who's being attacked, and is shot in the process. When he recovers and returns to the precinct, everybody who'd ragged on him is there to welcome him back, and they're all wearing the same Superman shirt. He still wears his, too, complete with the bullet hole.
The "boy with cancer" story is even better when you realize it was drawn by Tim Sale, best known for his collaborations with Jeph Loeb - whose son Sam Loeb died of cancer. And the art is close enough that if you wanted to, you could see the dad in the story as Jeph himself.
The finale of The Black Ring storyline in Action Comics. Lex Luthor, having gained the power of a god decides it's time to finally kill Superman and summons him into space for a final showdown, during which he learns that Superman is Clark Kent... and promptly LOSES IT, raging at the perceived injustice that Superman got to have parents like the Kents, while he had a scumbag like Lionel for a father. In the end, he has the choice to bring peace and happiness to the universe FOREVER... or kill Superman. And he just can't do it. He finally loses his mind as he realizes everything he's lost, not even knowing his own name.
It's not just that. Luthor, with the power of a god, decides to torment Superman with visons of loss, as he believes that Superman is so alien that he couldn't understand the concept. First he shows Superman how much pain the citizens of Metropolis felt when he was murdered by Doomsday, then showing his birth parents' final moments on a dying Krypton, then his loss of the person he called his son, Chris Kent (Lor-Zod) as he threw himself into the Phantom Zone to stop his bastard of a father General Zod and finally the destruction of New Krypton. Yelling at Luthor to materialize the most painful loss in his life, Luthor then shows the death of Jonathan Kent in Clark and Martha's arms. The realization that dawns upon Luthor is surprisingly painful.
Superman/Batman #76. Every damn page of it. The issue is from the viewpoint of Superman as he deals with the death of Bruce Wayne. The most touching moment is when Superman is talking to Wonder Woman. Clark is discussing how they'll outlive everyone they know and how they're higher beings. Diana stops him, telling him that no matter how he wants to rationalize it, he's just a man grieving for a lost friend.
Superman trying to end famine in Africa in Peace On Earth. He's a Physical God, he should be able to accomplish anything, right? He can't.
Recently in Action Comics, in which Supermanfails to save Pa Kent from a fatal heart attack, because Kandor was coming back to full size and he was mesmerized.
Equally sad is that after Pa Kent's funeral Superman actually fantasizes about going after Brainiac, the villain responsible for the whole damn thing, cornering him in his cell, and fantasizes brutally beating him to death. It's not only incredibly creepy to see Superman actually fantasize about killing someone, no matter how terrible, but the look on his face in the final panel of the fantasy that shows him realizing this won't bring his father back, just makes it even more heartbreaking.