In "Introduction to Film", the scene where Abed shows the video he made to his father. Relatively speaking.
This exchange between Abed and Jeff:
Abed: Jeff, I think you should play the role of my father. Jeff: I don't want to be your father. Abed: Perfect. You already know your lines.
This between Abed and his father:
Abed's' Dad: (tearfully) I never said I blamed you for her leaving. Abed: You never had to say it.
Most of the video is quite sad in itself. The video seems to be an allegory that he made about Abed's mother leaving the family, due to Abed's odd behavior, and the stress of her husband not caring for their child like she thought he should. Abed was put on several different medications and had his brain scanned, but none of it worked. Eventually, Abed's mother snapped, and he attributes all the blame to himself.
Most of Abed's Uncontrollable Christmas counts - Professor Duncan crosses the Moral Event Horizon over Abed dredging up memories of his deadbeat father; Britta is shunned by Abed for genuinely wanting to help him and being misunderstood.
Since this episode takes place after The Psychology Of Letting Go, this is the first Christmas both Abed and Pierce spend without their moms.
A lot of Abed's storylines, in fact. What starts out as a wacky Mafia parody with chicken ends with a reveal that Abed kept the whole thing going even when he could see it was going too far because he believed it was the only reason people were staying friends with him, and if he could get the balance just right they'd stay friends with him forever.
In "Aerodynamics of Gender" when Abed is bitched out by Meghan. What makes this moment so tear-jerking is not that she said it, but the fact that Abed wrote it, meaning that Abed really believes that he can't relate to anyone in some way.
Why is Pierce so obsessed with being the star of Annie's anti-drug play in "Celebrity Pharmacology 212"? Turns out as a kid his father replaced him in a Hawthorne Wipes commercial, and in an outtake where Pierce tried to be in the commercial, his father says to his face the replacement seems like a better son than him.
The study group won't let Chang join, even after he gets beat up by a group of children with baseballs for them.
The Dean's breakdown in "Documentary Filmaking Redux". Turns out he didn't even go to Greendale, he went to an actual university and he felt like he was ashamed of Greendale, and wanted to make it better.
"I don't... think I can finish my commercial... but I think I know how your documentary ends."
Pierce's home life. Before his mother died in the third ep of season 2 it was just him and her with maybe a few visits from his Jerkass father who passed down his prejudices. His seven marriages could be just his desperation to not be alone but for many reasons the marriages couldn't work, his "Super Fertility" is just a euphemism for being infertile (Which may relate to why he sees Jeff and Annie as his faux son and daughter), his friend Troy got to live in his mansion in season 2 for free before moving out (Since Troy's an idiot he had no idea that he was addicted to pills until it was too late) and didn't express much gratitude and from the season 2 finale that summer and most school breaks are just days to wait until the new semester.
Chang's Imagine Spot of him hanging out with the study group in "Accounting for Lawyers". He's in a Pop 'N Lock contest by himself because they were late and it feels like they abandoned him.
Especially since after all his hard work, the group rejects him anyway when they finally do show up. The single, pained tear running down his cheek makes it even sadder.
Britta's breakdown in "The Science of Illusion" where she tearfully reveals that she was behind the backfiring April Fool's prank that caused all the trouble in the episode because she just wanted to be wacky and fun like her friends for a change. Since they'd all been ragging on her for being a buzzkill (Jeff especially), they all look rather guilty. It then sets off a chain reaction of weepy confessions of feelings of inadequacy from everyone except Jeff and Abed, which are all quite sad — until, of course, we get to Troy's.
Britta: Knock, knock. Who's there? Cancer. Oh good, come on in, I thought it was Britta!
The end of season 2. Pierce makes a big speech about how he's so afraid people will reject him, that he mistreats anyone who gets close to him, which is what causes people to reject him, and how Greendale was the first place to ever accept him, and that this study group is the one that put up with him the longest. And then he leaves, and the rest of the group sits there waiting for him to walk back in. He doesn't.
Troy and Abed completely turning on each other in Pillows and Blankets. Abed sends an email to his troops detailing Troy's weaknesses - including his insecurity about his intelligence, and the fact that it's incredibly easy to make him cry. Troy tells Abed that he'll never get another friend, because nobody will have the patience with him that Troy had.
At the end of the episode, the two of them both want to keep fighting, because they're convinced it will be the last thing they ever do together. They would rather beat each other with pillows indefinitely than go their separate ways, but they don't see how they can just go back to being friends. Until Jeff intervenes.
Abed seems pretty upset (for Abed) in Regional Holiday Music, and he's desperate enough to spend Christmas with his friends that he resorts to recruiting them for the glee club pageant. It seems funny at first - and then you really look at him in certain scenes, like right before he and Mr. Rad start singing, and when he's apologizing to the rest of the group and saying he'll see them all after break, and he looks/sounds like he's as near to actually crying as he's ever gotten. And then you remember that last year, following a complete mental breakdown, Abed decided that the new meaning of Christmas for him is spending time with his friends.
Pierce sitting by himself in the middle of the carnival after Chang stops being best friends with him.
Abed: We're inside a locker. It's where I spent a lot of time in junior high.
Annie: You think this is where we'd put you? You know that's absurd, right?
Abed: Well, I'm not stupid. You can see I've upped the square footage. It's a metaphorical locker. It's a place where people like me get put when everyone's finally fed up with us.
Pierce being too afraid to stand up to his father in "Advanced Gay".
Gilbert Lawson discovering that his father never cared about him, and will only let him have the company if he agrees to never tell anyone who his father is.
To elaborate, Lawson is black and his father is Pierce's even more racist father Cornelius. So imagine spending your whole life mastering your father's game and winning and being presented with a legal document that makes it illegal for you to say who your real father is. All because it would tarnish the pure Hawthorne name.
It's made worse, after Gilbert refuses to sign the document saying he'll never tell anyone who his father is, and virtual Cornelius attacks him in response, by Gilbert's pained scream of "NOOOOO! I'M YOUR SON!"
The study group deciding to help Gilbert.
Pierce: We've been playing this game for a few hours. But you? You've been playing it your whole life.
Pierce then follows up with: "You took all his crap and you never even got to take his name. But now it's time for your reward, brother."
It's played for laughs most of the time, but Troy leaving the study group due to sacrificing himself to the Air Conditioning Repair School still feels pretty sad, particularly where Abed can't even face the study group anymore when he mentions that Troy told him as a parting word, "I know you hate this when people do it in movies."
Near the end of the Season 3 finale, when we see Abed destroying the Dreamatorium.
But also sort of heartwarming, as it demonstrates that he realizes that perhaps he has some maturing to do. And he did keep a few panels of it, and built a smaller one.
After watching "Curriculum Unavailable", everyone's anger towards the dean in "Course Listing Unavailable" becomes this. He sent his assistant home because she wore the same clothes as Annie, he made a little song for the gang during the announcements, he saved them pizza on pizza day, he just all around loves the group (to the point of great annoyance).
In "History 101", Abed realises their time at Greendale is ending and takes it that the group is splitting up, so he retreats into his mind where their life is a Sitcom with a Laugh Track and Status Quo Is God. The more things change in the cafeteria, and the closer Jeff comes to victory, the further in he goes.
Jeff revealing to his father in "Cooperative Escapism In Familial Relations" how supremely screwed up he is.
"I am not well adjusted. And more often than not, I am barely keeping it together. I'm constantly texting and there's no one at the other end. I'm just a grown man who can't even look his own friends in the eye for too long because I'm afraid that they'll see that I am broken. So you get credit for that. One time when I was in seventh grade, I told everybody in school that I had appendicitis. I wanted someone to worry about me. But when Beth Brennen asked to see the scar, I didn't want to get found out so I took mom's scissors and I made one. It hurt like hell. But it was worth it because I got 17 cards and I still keep them in a box under my bed 22 years later, because it proves that someone at some point cared about me. You wanna see the scar? (lifts his shirt) So. You get credit for that too. This is me."
In "Re-pilot", Troy signing Jeff's class action suit against Greendale. It's absolutely heartbreaking to see the show's most optimistic and positive character just break and see things as hopeless, and unlike Troy's past breakdowns, it isn't Played for Laughs.
The whole episode is pretty dark. The show deconstructs how difficult everyone's life was after graduating from an institution like Greendale. Britta's a bartender at a sleazy bar, Abed has retreated into programming as an escape, Troy is pretty much counting on his friendship with Abed to keep him going, Jeff's Crusading Lawyer plans crumbled and left him broke, Annie the overachiever is working in a deadend job. Arguable worst of all, Shirley's lack of real experience led her to lose money on Shirley's Sandwiches, which in turn led Andre to leave her and take the kids.
In all five seasons of Community there is no sadder moment than the quiet desolation in Shirley's voice when she says "Andre left me."
The stinger of "Introduction To Teaching" which starts off as a gag between Troy and Abed trying to play a prank on Jeff, only to find Professor Hickey entering to call his pharmacist about not being able to afford a better drug and then calling his mother to tell her that they can't afford to bury his father with the rest of his family. It's one of the more surprising cases of Mood Whiplash on the show, especially for a new character.
The entire "Mixology Certification" episode is pretty poignant for anyone who's struggled with alcoholism, or knows someone who has.
In "Basic Intergluteal Numinsmatics" Shirley tells Jeff and Annie that Pierce has died and the whole group is crestfallen. Especially Neil's tribute over the radio calling Pierce "One helluva D&D player".
The ending of "Cooperative Polygraphy", particularly Pierce's description of Troy, Troy deciding to take Pierce's offer and the resulting reaction from Abed.
The Reveal in "Geothermal Escapism" that the "Floor is Lava" isn't just a game to Abed. He is really seeing lava because Troy is leaving.
Abed calling himself crazy and admitting that it's embarrassing.
The whole goodbye at the end. And when Troy gets to Abed, you know that's when the tears will flow.
Meta example, but the following episode's opening credits, when listing the cast, has a notable jump where they cut out Donald Glover's name, and it continues on to the following episodes. Even though we knew he was leaving it was still sad to see. A similar sentiment can be said at the beginning of the season when Chevy Chase's name isn't featured.
Britta finding out her anarchist friends had outgrown her and probably never liked her.
Jeff being so insecure about turning 40 that he decided to down a bunch of scotch and shady Korean anti-aging pills, causing him to overdose and (briefly) fall into a coma.
In "Basic Email Security" we learn that Frankie emails her dead sister as a coping mechanism. The fact that it comes out of nowhere makes it hit a bit harder.
In "Intro to Recycled Cinema" Jeff confesses his fears to Abed that he will never leave Greendale and that unlike the other members of the group has nothing to offer the world.
Annie's critical take on herself and her relationship with Jeff in "Virtual Systems Analysis", after Abed correctly deduces that she's still hung up on that one kiss they shared nearly two years ago:
Abed (as Annie#2): Why are you blowing our magic moment with Jeff?
Annie: It's not magic. It's not even real.
Annie#2: But we love Jeff.
Annie: No, we don't. We're just in love with the idea of being loved. And if we can teach a guy like Jeff to do it, we'll never be unloved. So we keep running the same scenario over and over hoping for a different result.
Jeff trying to come up with something that inspires genuine passionate emotion within him by looking at his friends in "Basic Sandwich". The one thing that works is when he's looking at Annie and remembering the first time they came up with the "milady"/"milord" in-joke way back in "Football, Feminism, and You". Made very sad by the fact that Britta (at this point Jeff's fiancée) is also in the room but elicits no particular emotional reaction from him, while Annie has just made it clear she's given up on trying to make their relationship go somewhere and is just letting him deal with his choices, even if they're bad for him. The saddest part, though, is that Jeff refuses to divulge what he thought about - leaving Annie still under the impression that Jeff is basically indifferent to her, Jeff presumably having taken Annie's refusal to chase him any more to heart, and only the audience having realised that maybe Jeff actually is as hung up on Annie as she has been on him all this time.
Abed's speech about TV in "Emotional Consequences of Broadcast Television".
Abed: TV defeats its own purpose when its pushing an agenda, or trying to defeat other TV or being proud or ashamed of itself for existing. Its TV; its comfort. Its a friend youve known so well, and for so long you just let it be with you, and it needs to be okay for it to have a bad day or phone in a day, and it needs to be okay for it to get on a boat with Levar Burton and never come back. (voice cracking) Because eventually, it all will.
The way Jeff and Annie leave things in the last episode is at once perfect and absolutely heartbreaking. Jeff finally admits how he feels about her, but also admits - to himself and her - that he doesn't fit into her life right now.
Jeff: I let you go, Annie. With my hands, and my head. The heart - which cynics say is code for penis - wants what it wants. But I let you go.
Annie: The others are coming. I think... you should kiss me goodbye or you might regret it for the rest of your life.
Jeff: What about you?
Annie: (wryly) I'll regret the kiss for a week. I'm in my twenties. Who cares? (The Big Damn Kiss)
At the end of that same episode, Jeff hugging Abed twice.