In "A Long Walk to Pittsburgh", Eric catches Shawn kissing Topanga. It turns out to be innocent because her family's moving, but before that is discovered we get a nice glimpse of Big Brother Eric when he slams Shawn into a wall:
"You think you can do something that causes Cory pain, you're not gonna get pain back? You don't know what's going on."
Also from "A Long Walk to Pittsburgh", this exchange:
George Feeny: "I believe that when you find love, you hold on to it and cherish it because there is nothing finer, and it may never come again."
Feeny: [steps forward as well] "George Feeny, I'm Topanga's teacher."
Curtis: "Well, I don't know that I appreciate what you are teaching these children, sir. To plant wild ideas about true love in young undeveloped minds is as irresponsible as my sister and brother-in-law ripping her from the only environment she's ever known. At this... delicate time."
Feeny: "Madam, if you choose to question my opinions, then you disregard 38 years in the public school system, where I have born the responsibility of those opinions for 30,000 students. None held in higher regard than Mr. Matthews and Ms. Lawrence."
Cory Matthews: [sits up excitedly] "You like me?"
Feeny: "Stay out of this."
Nurse: * Stopping Shawn as he, Cory & Topanga head into the ICU to see Joshua* Oh I'm sorry, it's family only.
Alan: He is family.
"Santa's Little Helpers" (Doubles as a Tear Jerker and one of Will Friedle's finest performances):
Eric: * sitting alone in the snow* ..."I want to make the happiness of the entire world my responsibility." What an idiot, what am I supposed to do? I made all those little kids smile, took care of everybody that came to see me... No disrespect, but why would you send me that little boy? Why doesn't that nice little boy have parents? Why doesn't that nice little boy have parents? Why did you send me that little kid? ...And why do I only come to you when I need something? I guess you shouldn't have to take care of everything, right? I can take care of this. I can be responsible for the happiness of one little boy.
Eric taking Tommy home with him so he can spend Christmas with the Matthews family.
Eric and Mr. Feeny talking about his retiring
Eric: "Mr. Feeny? If I'm really quiet... will you stay?"
Cory and Morgan rarely interacted, but there is the first season episode "Risky Business" where Cory leaves Morgan alone and panics when he comes home to find the window broken and Morgan gone, thinking she's been kidnapped. Then he and Morgan have a nice little talk in the tree house.
Eric finally getting into college at the end of season four, even the audience cheered.
The finale has Jack & Shawn sharing a moment, after Jack remarks that he doesn't care that his step-father's cutting him off (Jack decided to go into the Peace Corp rather work for his step-father) because "Money doesn't make you rich, life does. Our father taught us that."
A second one comes when Ghost!Chet appears between his two boys, and remarks "I never said that, that's stupid! MONEY makes you rich!" But upon hearing Jack remark about going into the Peace Corp, he looks up and says "That's the sort of thing they like up here", before proudly looking at his boys. He then grabs Rachel's ass.
Eric throughout "Seven the Hard Way." The rest of the group is letting current, very bitter disagreements drive them apart, but Eric remains resolute in forcing everyone to work things out and stay together. This is brought to the fore by him imagining what things would be like if he fails, where his future-self has one philosophy: "Lose one friend. Lose all friends. Lose yourself." When asked why he didn't write any more than that, Eric replies, "Nothing else seemed important.
Another one follows shortly after this scene where Mr. Feeny turns to Eric and says "You were always one of my most interesting students, Mr Squirrels."
Eric again in "Can I Help to Cheer You?" Eric's young orphan friend Tommy has been adopted, but will have to move to California. Tommy would rather stay with Eric and vice-versa. However, Eric realizes Tommy would be better off in California. When Tommy begs to stay with him, Eric lies about not wanting Tommy. It's a Tear Jerker for Eric, but also a CMOH, as it shows how much he has grown up and how willing he is to put his own happiness aside for someone else.
The end of "The Psychotic Episode". Corey's been having dreams about killing Shawn so Feeny suggests finishing the dream (he always woke up as he was killing Shawn). He ends up the entirity of the group by throwing them down the elevator shaft, except for Topanganote And technically Eric, who jumps after Rachel after Cory throws her, who shows up in a wedding dress. When he wakes up, he tells Shawn he's afraid about things changing after he gets married.
In the episode where Shawn uses Feeny's house as a B&B, Feeny tries to get a couple who haven't checked out yet to leave his room, believing they are a young couple. They are revealed to be around Feeny's age. "I was young once! Maybe I still am..."
The romance between Mr. Feeney and Dean Bolander. Watching William Daniels and Bonnie Bartlett (one of Hollywood's most successful marriages in Real Life) blush and fumble around each other like high schoolers is sweet.
And the very apparant shipping of the couple by Cory & the rest of the group.
Their marriage vows in "State of the Unions" are just the cutest, sweetest thing in the whole world, not to mention a tremendous testament to the power of love and lifelong commitment.
Feeny: Quietly, I have searched for love for most of my life. And now that we begin this marriage of our spirits, I realize how incredibly lucky I am to have found it.
Lila: My only sadness is that I found you so late in life — that we've lived our lives spending more days apart than together.
Feeny: But you've given me your love and friendship, and I promise that I'll make up for that lost time.
Lila: For marriage is based on those things, but — friendship most of all.
Cory asking Topanga to be his girlfriend in the season 3 premiere.
Shawn telling Cory his half-brother Eddie is "only blood" and that Cory is his real family.
Mr. Turner offering to take Shawn in while his parents were on the road chasing and running from each other.
Shawn wishing Minkus a Merry Christmas in season one. Keep in mind what their relationship usually is.
The finale, when the class sits in Mr. Feeney's room and asks him to teach them one more time
Mr. Feeney: Do good. Topanga: Don't you mean 'do well'? Mr. Feeney: No.
The very last line of the series. I love you all. Class dismissed.
Topanga's family moves from Philadelphia to Pittsburgh. In the next episode, she shows up on Cory's front porch in the rain. If that's not love...
And then Corey's speech to his parents about what he thinks love is.
Cory: All I understood was that she was the girl I sat up every night thinking about, and when I'm with her I feel happy to be alive. Like I can do anything. Even talk to you like this. So that's, that's what I feel is love, Mom... When I'm better because she's here.
The Group Hug between Cory, Shawn, Topanga and Minkus in the graduation episode.
After Shawn turns up drunk at Alan's birthday party in "Family Trees" following Chet's death, and the midst of a Heroic Blue Screen of Death over the fact that he doesn't have any parents, Alan & Amy promptly offer to adopt him, citing that he's pretty much family anyway. He turns them down because he doesn't want to disrepect Chet's memory, although he does ask Alan to yell at him like he does to Cory & Eric.
Shawn's speech to the sickly baby Joshua in "Resurrection" doubles as this and a Tear Jerker.
"Sometimes the things we complain most about are the things we care most about. Unfortunately, sometimes we don't realize this until it's too late."
"Lose one friend, lose all friends, lose yourself."
Topanga's sudden proposal to Cory at the end of "Graduation," which, in itself, she did out of fear they'd go their separate ways after high school. Then, Cory ceremoniously proposes to her later- although there's no spontaneity involved in it and it seems a little pointless now.
In "Janitor Dad," Chet gets a job as the school janitor to provide for the family. An embarrassed Shawn eventually asks him if he's okay picking up other people's trash.
Chet: Well, it has this amazing benefits package. Shawn: What benefits are there to being a janitor? Chet: Well, for one thing, after bein' on the road a year away from my son, what better benefit than a job that lets me be near him?
After getting over his embarrassment, Shawn takes Chet's mop and cleans up a mess himself.
Chet: Um, you don't have to that, Shawn. Shawn: I know I don't, and I know you don't, either.
Tommy telling Eric in "Resurrection" that he wants to go & see Joshua in the hospital, since if Joshua is Eric's little brother, that means that he's Tommy's little brother too. The look on Will Friedle's face after that line pretty much sums it up.
Cory telling Topanga "I remember everything you say. It's important to me." after he mentions something she said years ago.
Chet & Jack meeting for the first time since Jack was a little kid, with Chet being so proud that he has a son in college.
In the Grand Finale, Eric muses that after he moves to New York he'll be able to anyone he wants to be. Topanga proceeds to sincerely tell him that she wants him to be Eric.
Eric, deciding to demonstrate his lucky penny, asks a member of the football team if "As an athlete on the football team, is it distracting being gay?". There's a pause, as the scene seems set-up for him to try & attack Eric only for Jack to take the abuse... Only he happily thanks Eric for outing him since he's been holding it for so long, before turning to his teammaters & admitting that he's gay. And then the rest of the team say it's no big deal - They're all gay.
Season 4's Thanksgiving episode, "Turkey Day", which revolved around the class differences between the Hunter & Matthews families as the Hunters host the Matthews & both parents lack of comfort in the situation, only to realise it shouldn't matter when they see the kids sitting down & having dinner with Frankie & Herman Stecchino.
From "Career Day" in season 2: "I was thinking I was the son of a grocer, but who I really am is...the son of my father."
From "Easy Street", the scene in which Shawn rather shyly presents Cory with an expensive engraved watch, overjoyed at being able to afford a decent Christmas present for his best friend for once. Also, the entirety of the extended scene between Cory and Shawn at the end outside in the snow where Cory begs Shawn to come home, Shawn breaks down and confesses how afraid he is of wasting his life, and they simply discuss the spiraling-out-of-control situation and try to wrap their minds around the issues presenting themselves. Especially this part, in reference to the Robert Frost poem "The Road Less Traveled", which Cory mentioned earlier in the context of making huge, all-important, defining, life-changing choices:
Shawn: Well...two roads diverge in a wood — and I choose the one that leads back to your house.
Alan sending 60+ telegrams to baseball player Jim Abbott to get him to come talk to Cory about chasing your dreams after Feeny (probably unintentionally) ruins Cory's aspirations of becoming a Phillies center-fielder...and it works!
"She's Having My Baby-Back Ribs". Everyone telling Topanga that she isn't fat and that she's perfect the way she is is heartwarming by itself, but what's really moving about this episode is Cory's reaction when Shawn mistakenly tells him that Topanga's pregnant, and the way his parents react to it as well. At first, he's understandably scared, and goes to seek advice from them. Mr. Matthews is a little angry but quickly calms down, and he and Mrs. Matthews talk to Cory about how wonderful raising a child would be for him and Topanga, along with the responsibility that comes with being a parent. Cory then tells them how happy and excited he is for Topanga and himself, and goes home to celebrate with her (but she isn't actually pregnant, of course). Not only does this scene show how good Mr. and Mrs. Matthews are as parents, but it shows just how supportive and loving Cory is to his wife.
Arguably, the whole series counts. Just seeing all these characters grow up together and mature, from childhood to adulthood.