Splinter accepting April as his daughter at the end of City at War.
Splinter's heart attack in volume 4, issue 10, and his funeral in issue 11. Seeing as Splinter was a father to the Turtles, it's completely devastating.
Leo's eulogy in the latter issue is both touching and heart-wrenching, capping off with "But we will never forget him—our sensei, our master... our father."
Cold, Cold Ice is a depressing revenge attempt that humanizes the Foot.
Gabrielle's death during childbirth. Casey was just starting to re-build his life without the anger and insanity that previously plagued him only to have it shattered in one blow. The silver lining is that he got Shadow out of it.
Dark Shadows. It's set in a Bad Future with Casey Jones' adopted daughter Shadow as a scarred, hardened warrior on a flooded earth. She seeks out Raphael, her apparent ninjutsu instructor, in an attempt to unleash her rage on him and almost kill him, and Raphael expounds that what ultimately drove the family apart was something SHADOW did to Donatello (it isn't explained what), and she takes out his eye before choosing to spare him. Then it shows that this is all a vision shown to present day Raph by Time Mistress Renet - as the GOOD outcome. If Raphael doesn't train her in ninjutsu and set her down this path, she'll die at the age of 23 at the hands of The Foot. Raph makes the decision to train her.
Sons of the Silent Age. It takes place shortly after the Shredder's death, with the Turtles feeling restless and aimless, not to mention having the Foot swearing revenge against them, which would continue to haunt them for some time. While on a rafting trip down a river with Casey and April, they encounter a dying fishlike humanoid covered in radiation burns from the nearby nuclear plant, who communicates mentally with April, and reveals that she is the last female of her kind. The other four remaining humanoids, four males, soon show up and fight the Turtles, thinking they are hurting the female, but the fight fizzles out after she dies. The four takes her body back with them to the waters, doomed to extinction. The End.
And that's not even mentioning the comparison the story draws between the four remaining humanoids, and the Turtles, both doomed to extinction.
"The Path", from Volume 2 of Tales. In particular, the shot of Mikey cradling his dying cat in his arms and saying "Goodbye, friend."
A flashback shows Splinter having a vision that somehow involves Mikey and death. A conversation ensues about steeling against love and compassion in order to survive. In the present, a ritual can be performed to save Klunk's life and Mikey is prepared to use a stray cat he found. He tries to justify what he's doing by saying, "Nobody loves it"—only to recoil in shame with what he just said, so he has the stray released, even if it means losing his friend. In the end, Splinter admits that Mikey's way of compassion is something he could learn from.
A minor one, after the scuffle with Casey Jones who then calls Raph a freak before running off, the scene leaves a clue as to why Raph is always so angry. Raphael is wrestling with the fact that he can't live a normal life, and that he's an outsider and unlike the rest of the human population. He's mad that he has to be an outcast for looking so differently. And when Casey Jones calls him a freak, Raphael's reaction says it all. It really shows that it hurts to be judged on looks for someone who's already an outcast.
Also that he's the only one among the brothers to feel this way. Which could be why he would often fight with his brothers (especially Leo) cause they don't feel the same way and don't understand his feelings. So he has no one (except maybe Splinter) to talk to, so he bottles it all up.
Raph's reaction to coming home and finding the lair in shambles, and Splinter gone.
Donatello falls to his knees in pure, broken, sorrow.
And when they return to April's, for once they really do seem like lost, scared teenage boys who need someone to turn to. They're only 15 - and they're facing something very tragic and traumatizing.
The fate of Master Splinter's owner Yoshi, poor sap.
As if that weren't enough we see a pre-mutated Splinter holding his dead master's hand in grief. Any other rat in his situation would simply eat the corpse, but this one loved him.
"Then he was gone, and I was alone."
This Shredder really likes to twist the knife in the wound whenever he gets an opportunity. It doesn't matter who, as long as he gets the chance.
Raph: Where's Splinter?
The Shredder: ...Ah! The rat! So it has a name... (evil smirk) It had a name.
Splinter:I am proud of you, my sons. Tonight you have learned the final and greatest truth of the Ninja: that ultimate mastery comes not of the body, but of the mind. Together, there is nothing your four minds cannot accomplish. Help each other, draw upon one another, and always remember the true force that binds you. The same as that which brought me here tonight. That which I gladly return with my final words: I love you all, my sons.
Mikey is crying the hardest in that scene, which paints an earlier scene in a vastly different light. Earlier in the film, as Mikey and Donnie wait for the pizza to be delivered, Donatello contemplates what it would be like once Splinter dies. Just the way he says it, avoiding any words to do with "death", can make the eyes of anyone who has a strong bond with their parents misty. But the way Mikey shrugs the subject off... at first watching, it seems like Mikey is just not paying attention, but on subsequent viewings it's clear that Mikey is in denial - he can't bear to think of a life without his father beside him.
Leo and Raph's argument. It seems to be a Running Gag since Donnie and Mikey head straight for the kitchen. However it becomes less comical after Raph is knocked unconscious and Leo is fending the Foot off long enough so they escape to a hideout. As they hide, Leo stays by Raph's side until he wakes up. It doubles as heartwarming but you can feel the guilt Leo is going through since his brother almost died after their fight (which ends with Leo screaming the team doesn't need Raph). When Raph wakes up he is most overjoyed.
When Leo is about to be killed and Shredder tells the other three to forfeit their weapons to save his life, even though he knows Shredder is full of it, Raph is the first to chuck his sais
Splinter and Danny's conversation while the former is kept prisoner at the Foot Clan base.
Splinter: And have you no one to go to, Danny? No parent?
Danny: My dad couldn't care less about me.
Splinter: I doubt that is true.
Splinter: All fathers care for their sons.
(He trails off, clearly thinking about the turtles.)
Danny and Charles' reunion. Also falls under Heartwarming.
Danny: Dad, I'm fine. And Dad, it's just Dan now, okay?
(Father and son share a tearful hug.)
Despite Raph's impatience, the other Turtles willingly wait for any information on the Foot via April's news report, hoping it'll help them find Splinter. Unfortunately, all they got is a call from April's boss telling her, out of the blue, that she's fired (all thanks to Chief Stern).
April: My amazing new friends have suffered their first real defeat. That's bad enough, but they also lost the opportunity to find out about their mentor, and I'm sure that hurts them more than anything else.
Splinter's flashback to the death of Tang Shen and his loss of Miwa.
The ending to "The Gauntlet." Seeing all the turtles actually lose to Shredder.
The ending to "New Friend, Old Enemy"
Timothy/Pulverizer, the well-meaning but comically inept Turtle fanboy. He wanted so desperately to become a mutant like his heroes... It turns out that he does - in the worst way possible, becoming nothing but a gelatinous blob filled with organs - this universe's version of Mutagen Man.
Pretty much everyone predicted that Shredder's adopted daughter Karai was actually Hamato Yoshi's biological daughter, Miwa. This didn't stop Splinter's reaction when he found out the truth from feeling like a punch to the gut for viewers everywhere.