This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Following
Jacob kills Paul in order to spare him the pain of a long, drawn-out death.
Towards the end of the first season, Jacob begs Emma to run away with him, realizing that he's not cut out to be a Follower. Emma slashes his throat.
The death of Debra Parker.
In the beginning of the second season, the look on Ryan's face when he finds out that Claire is dead is pretty devastating.
In "Teacher's Pet", we see the other end of that situation. Claire is devastated when she realizes she needs to disappear and can't even tell Ryan she's alive. The grief-stricken way she says, "I can't do this to him" is heartbreaking.
In "Sacrifice", Mike realizes that he's not OK, having nearly killed Luke in a rage, and decides to head home rather than risk becoming like Ryan. But then Max is kidnapped, and Mike, being the guy that he is, cancels his plans to help Ryan find her. After they rescue her, Ryan gets a video message from Lily. Convinced that Mike killed Luke, she's attacked his family home and killed his dad. The episode ends with Mike breaking down and crying and Ryan just holding him...
A minor one, but in "Teacher's Pet", Ryan does his damnedest in trying to save the life of Mallory, a Korban cultist, after her throat had been slashed by another cultist. She even intended to give herself up. Another moment comes from when Carroll casually kills a cat, leaving Mandy in tears.
Mandy hands herself over to Lily, thinking that she'd be safe. Lily decides to let Luke and Mark play with her instead. Poor Mandy. All she really wanted was for someone to love her...
To make matters worse, even Joe is visibly devastated by her death. Joe. Just let that sink in.
Joe publicly humiliating Kingston Tanner before trying to persuade him and his son to kill each other. Kingston chooses to kill himself to save his son. And then Joe kills his son anyway.
It gets worse. In most sects of Christianity, suicide is considered a mortal sin, and being a preacher, Kingston is fully aware of this. the man was willing to risk eternity in Hell to save his son's life.
After all of Ryan's efforts to save her from the twins, Claire tells him they can't be together.]
The flashback of Mike leaving Max to hunt down Mark, with her at first begging him not to go, and when he says he'll call, telling him not to. After all they went through before getting together, seeing it crumble in that one moment was gut-wrenching.
Theo being forced to kill his wife and leave his family behind. He crossed the Moral Event Horizon for sure, but the look on Theo's face before he goes through with it just shows how much he truly cared for them and that he doesn't want to do it—he has to.
Joe Carroll's death is a strange mix of this and Crowning Moment of Awesome. He certainly deserved to die after everything he did, but seeing him limply spasm around on the execution table before settling down in silence, followed by Ryan being so emotionally devastated that he returns to drinking and hallucinates Joe next to him... It's almost heartbreaking. Almost.
Mark and Daisy explaining their brief history. Mark had no friends growing up (except for Luke, of course, whom he was always with). Daisy, however, had hundreds of friends, but it wasn't until she met Kyle that she realized how shallow her "friends" were and that she was just as lonely as Mark was. It really makes Kyle, Luke, and Lily's deaths all the more tragic.
Ryan's false death after killing Theo Noble. Everyone, from his pregnant girlfriend to the friends who've served by him for three seasons, to his niece is led to believe that he is dead. And if Ryan wants to take Eliza down, he can never even hint otherwise.
A meta example: FOX unexpectedly cancelled the show, making the current season the final one.