Debbie crying when their fake "Aunt Ginger" has to go back to her home.
Lip's summation of his mother to Ian: "You know how Dad's a total fucking asshole?" "Yeah?" "Turns out he's the good one."
Fiona breaking down crying as she yells at Monica for leaving them.
Karen and the other teenage women being forced/pressured into the "purity confessions" and being told that they have to "repent" for being sexually active, particularly the one who only participated in a sexual act under threat of being assaulted with a pipe, but is still told that she has sinned.
And as an extension of this, Eddie's suicide is this as well. Yes, he could quite frankly be considered a monster for his treatment of his daughter, but when he realized that Frank wasn't really having sex with her willingly, he considered why his daughter would be doing that to get back at him and in turn realized how much of a horrible person he'd been, and due to his moral absolutism, he took his own life out of guilt.
Seeing Claire, a woman who is much younger than her peers in the old person home, try to hold back tears during Excursion Day, as well as pleading to do something interesting instead of visiting the CVS.
Surprisingly enough, Frank breaking down and crying, and even going back to Monica after his mother's death.
Fiona's discovery that Monica and Frank stole all of her savings is just...heartbreaking.
Fiona's tantrum at the end of A Great Cause is one of the most beautifully tragic moments on television. After Fiona sees all the repercussions for trusting Monica with her responsibilities and trying to have a life of her own, she has a short but epic tantrum in the kitchen. She stops herself and then she goes right back into routine, being the motherher own could never be.
Fiona shouting at Monica to wake up when she refuses to get out of bed for days during a low swing. Made worse when Debs and Ian try to bring her food, but she refuses it. Made even worse when Monica tries to commit suicide during Thanksgiving dinner.
When Lip finds out Karen's baby isn't his.
The immensely melancholy opening scenes of the second season finale.
The fact that Monica had an opportunity to receive therapy and recover from all of the crazy, and it was destroyed because of Frank's selfishness.
The end of the second season. There is very little happiness to be found there.
Karen abandoning Sheila.
Season 3 doesn't let up on the tear jerking moments either. The first episode of the season has Estefania spend most of the episode mourning over Marco after her father shoots him point blank. Though this may double up as a CMOF.
There's Lip's message to Karen and it looks like he's going to break down into tears.
In the Season 3 finale we get to see Carl's unconditional (and arguably, undeserved) love for and faith in his father when he shows up at the hospital to shave Frank's head to "let the sun rays in" to heal him, just as Frank had told him earlier that season.
In Emily, Frank, delirious after surgery see's the titular little girl and fellow hospital patient, as a younger version of Fiona. He shows genuine remorse for his behavior, and Emily plays along with the conversation as Fiona. At the end of the episode, when it appears Emily is about to die, Frank's reaction is heartbroken, because as far as he can tell, he is watching his daughter dying. Doesn't help that the real Fiona is in prison throughout the episode.
It doesn't help that Emily plays along partially because her own father abandoned her after she fell ill and this gave her the opportunity to imagine having a father that will take her on all sorts of fun adventures when/if she gets better. It's a double punch in the gut when she dies and never gets that chance.
In the Season 4 finale, Ian enters a deep depression revealing his bipolar disorder. Mickey is near panic, and when it is explained to him by Fiona he flatly refuses to have Ian locked up in a mental hospital. He wipes away tears and his voice cracks as he asserts that they are all going to take care of Ian in the Milkovich house and nobody is taking Ian away from him.