Mr. Feeny: Champions of what, Mr. Matthews? Of a generation whose verbal and mathematical skills have sunk so low, when you have the highest level of technology at your fingertips? Gutenberg's generation thirsted for a new book every six months; your generation gets a new webpage every six seconds. And how do you use this technology? To beat King Koopa. And save the princess. Shame on you. You deserve what you get.
And then the bell rings. As the kids go to leave, he flips and tells them to "sit down!", solemnly declares "For the first time, I choose to walk out on you," and leaves the classroom.
Cory: Listen, Keiner, this is between me and Shawn, so take your greasy head and your rat-faced thug and get away from my friend!
"And Then There Was Shawn" is a beautiful send-up of the slasher genre and Scream.
Near the end of "Chick Like Me," after being constantly touched and felt up by Gary, "Veronica" (actually Shawn) is accused of liking girls instead of boys because she won't let him touch her. She growls "As a matter of fact, I do," then repeats it before she punches him off his feet and comments "For every girl I've ever known" when asked why she punched him. Then she leaves with Topanga and Cory (Cora) to go write an article about the experience, therefore spreading the word about Gary's grabby hands to the whole school.
Alan: (to Mack) No, listen, you see! A judgment I made a long time ago is that Shawn Hunter is the best friend that my kid ever had. And I will kill to protect Shawn Hunter from people like you.
In "Learning to Fly," Eric's speech to Dean Bolander about how he needs to go to Penbrook University, saying that he wants to live up to the potential everyone says he has and that if the college doesn't let him do that, then it's the one not living up to its potential. Especially when it turns out that it convinced her to grant him admission to the school. The studio audience outright cheered at that point.
Really, the entire arc Eric goes through in Seasons 3 and 4. He doesn't put the work in during in high school, and finds himself rushing to get his grades high enough to get accepted into college, only to fail for that exact reason. Come Season 4, and after struggling with adjusting to life after high school, he then makes the effort to get into college, and that speech is the culmination of the arc and the pay-off to Eric being crushed when he reads his rejection letter the prior season.
There is one little thing that makes it better, and it's that, at the end of Season 3, Eric is rejected from a "safety school" (a college where almost anyone gets in and little is required of the students), only to get into the far more prestigious Pennbrook in Season 4.
In "It's About Time," Eric hijacks an extremely glitzy wedding (said to be the social event of the year) from a disposable diaper mogul for Cory and Topanga.
When Griffin arrives at John Adams High, he proceeds to immediately get dates with several of the hottest girls in school within minutes. Later, after rebuffing Frankie and Joey's offer of being his lackies as he has no need for them, he's confronted by several angry members of the football team. After Griffin is challenged to step outside, Frankie and Joey step up and say they would love to go outside and talk. When the jock states it's between him and Griffin, Frankie gets the absolutely badass line "No. We're between you and him."
Cory, Topanga, and Shawn go to the school to stop vandals from trashing the school. They assume Shawn's there to join them, but when the vandals hand him the spray paint, Shawn knocks it out of the guy's hand, quotes the First Amendment (he accidentally read the chapter), and credits Feeny as the reason he's not with the rest of them.
Eric teaching a group of immigrants and earning Feeny's respect, despite disobeying him earlier that episode.
The escalating pranks in "The War." Shawn and Cory park Rachel's car in her dorm room, so Rachel, Angela, and Jack retaliate by planting super glue on the desk chairs of Shawn, Topanga, and Cory, dousing them in honey, and letting a bear into the classroom. The trio rip themselves free and jump out the windows. Feeny finds it hilarious - and misses the opportunity for an Exit, Pursued by a Bear joke.
The show portraying the interracial relationship between Shawn and Angela as no different than any other relationship, with not a single mention of it being such a relationship.
In "Everybody Loves Stuart," Cory shoving Stuart into the door after he finds out that Stuart had been hitting on Topanga (and that it had made Topanga extremely uncomfortable). The build-up to it is what really sells the moment.
Feeny showing his Badass Teacher colors during the meeting to determine Cory's fate. Stuart, unfortunately, isn't too intimidated by the older teacher, who tops the moment with this line:
Feeny: Can I rip off your head and roll it down the hallway?
Dean Bolander's speech to Stuart after she suspends Cory for one day.
In "By Hook or By Crook," Feeny puts Miss Hart in her place after he finds out that she gave Eric the answers to the exam and she expresses offense to his remark that "this is what I get for hiring a pretty teaching assistant," followed by the following exchange.