The rare occasions when Emily and Richard stick up for Lorelai, notably:
Richard going ballistic on Staub Hayden - knocking Staub's drink out his hand, grabbing him by the lapels, and towering over him - for blaming Lorelai for all of Christopher's failures, in season 1, episode 15.
Emily telling Christopher to leave after he yells at Lorelai in season 3, episode 2.
Emily verbally eviscerating Mrs. Huntzberger in season 6, in the episode "We've Got Magic to Do." Here's the whole scene, truly a sight to behold.
Emily: So Richard tells me we have a little problem. Shira: Really? With what? Emily: With the kids. Logan, Rory. I understand you're not exactly thrilled with the match, that you let that be known to Rory at the dinner she had at your house. Shira: Oh, well, I wouldn't say "not thrilled". Emily: Then what would you say? Shira: Oh, Emily, this is a party. Emily: I'm just curious. Shira: This may not be the time and place, Emily. Emily:(to two guests walking by) Hello, you two, drop by our table later. (back to Shira) Let's make it the time and place. Shira: Consider the discrepancies, Emily. Emily: Well, that's what's confusing me. They both come from good families, both have good values. Money doesn't seem to be an issue. We all have money. Shira: Frankly, Emily, there's your money, then there's our money. Emily: Oh? Shira: And our family has a lot of responsibilities that come with that. An image to maintain. Emily: Ah, yes! Well let me tell you this, Shira. We are just as good as you are. You don't think Rory is good enough for your son, as if we don't know Logan's reputation. We do. But he is welcome in our home anytime, and you should extend the same courtesy to Rory. Shira:: Emily... Emily: Now let's talk about your money. You were a two-bit gold digger, fresh off the bus from Hicksville when you met Mitchum at whatever bar you happened to stumble into. And what made Mitchum decide to choose you to marry amongst the pack of women he was bedding at the time, I'll never know. But hats off to you for bagging him. He's still a playboy, you know? Well, of course you know. That would explain why your weight goes up and down 30 pounds every other month. But that's your cross to bear. But these are ugly realities. No one needs to talk about them. Those kids are staying together for as long as they like. You won't stop them. Now, enjoy the event.
Richard gets his own moment in the same episode as the above: After finding out that Mitchum did indeed destroy Rory and casually brushing it off Richard goes into full on Papa Wolf mode, breaking his normal stoic demeanor to call Mitchum out. He then admits Lorelai was right to Emily, leading to the above.
Mitchum: It was just business Richard. Richard:(absolutely furious) You destroyed that girl!
Rory gets her Balalaika's out on Emily.
Lorelai reenacts the ending of Season 5 and ends up reinstating Friday Night Dinners. Doubles as a Funny Moment.
The brutal fencing duel between Rory and Paris in season 3.
Every fist fight in the show.
Literally everything Dave does in order to date Lane: spending 5 straight hours playing hymns, giving a detailed explanation of why he's a decent person to Mrs. Kim, reading the entire Bible in ONE night.
Luke vs. Christopher finally coming to blows in Season 7...in the town square...amidst all the Christmas decorations...without a single word spoken by either of them...
In Season 5: Luke calling Chris out on never being there for Rory, and that he was more of a father to her.
Paris tearing into Logan (Rory's slacker boyfriend) in season 6.
"You, Logan Huntzberger, are nothing but a two-bit, spoiled waste of a trust fund. You offer nothing to women, or the world in general. If you were to disappear from the face of the earth tomorrow, the only person that would miss you is your Porsche dealer."
Logan: You should send me a copy. Jess: Sure, where do I send it? The blonde dick at Yale?
Made even funnier, as Logan has been harassing Jess all night to no avail. Jess opens his mouth once and boom. It only takes a few words.
Followed by Jess walking out and confronting Rory about the mess she's made, voicing the thoughts of viewers all over the world.
Jess: This isn't you! This! You going out with this jerk, with the Porsche! We made fun of guys like this! Rory: You caught him on a bad night. Jess: This isn't about him! Okay? Screw him! What's going on with you? This isn't you, Rory. You know it isn't. What's going on? Rory: I don't know... I don't know. Viewers: FINALLY!
Made even better, as, because of his words, Rory reunites with Lorelai and goes back to Yale.
Jess' return itself is a CMOA. Before he was a high school dropout, screw up and no one except Rory and Luke believed he'd amount to anything. In Season 6, he's turned his life around, is a successful writer and businessman running his own bookstore and gallery. Now he's the one inspiring Rory. Imagine Taylor, Lorelai, Dean and Stars Hollow's reactions.
Let's just say in season 6 Jess is a living, breathing CMOA, and leave it at that.
The judge in Season 6 sentencing Rory for stealing a boat and giving her a speech about how she respects law and doesn't tolerate rich brats who feel entitled to ignore it. Just after Rory bragged she's going to Yale (despite technically having dropped out) in hope of impressing said judge, and her rich grandfather and his lawyer had assured her they had everything under control. And the judge gave her a punishment about five times harsher than they expected.
Luke's words to Kirk when the latter is trying to be cool and saying Lulu is smothering him and he wants to break up with her and be a dick-swingin' bachelor.
Luke: Listen, you pinhead. You should be kissing the ground that Lulu walks on. Why that sweet girl lets you within a hundred miles of her is beyond me, but she does. You are the luckiest man on the planet to have a girl like that looking out for you and caring about you, and if you say so much as one unkind word to her, I'm gonna personally break every bone in your body.
Rory ripping into Mitchum over the phone for not coming to see Logan in the hospital.
"I just thought I'd call and remind you that Logan is lying in a hospital bed with a partially collapsed lung and a whole host of other potentially life-threatening injuries. And Im figuring a guy like you, surrounded by nothing but a bunch of terrified sycophants might not have someone in his life with the guts to tell him what an incredibly selfish, narcissistic ass hes being, so I thought I'd jump on in. Swallow your pride, get in your car, and come down here and see your son, now!"
Luke asserting his right to see April to April's mom during Season 7, Anna Nardini. One of the few times when Luke gets passionate about something he cares about, and doesn't hold back.
Rory verbally smacking down Paris (who has just given her a lame assignment for the school paper because of a petty grudge) in "Nick and Nora/Syd and Nancy", all without ever losing her polite smile:
After failing to get back with Lorelai after she broke up with him over refusing to elope with her and halfheartedly trying to later, Lorelai admits to drunkenly sleeping with Christopher after breaking up with Luke, and Luke drives all the way to Christopher's just to PUNCH HIM IN THE FACE. After everything Chris did in the previous season and what he'd just done, it was immensely satisfying.
After Emily's machinations result in Lorelai and Luke's breakup, Lorelai cuts her mother out of her life entirely, while Rory, who is obligated to see her grandparents due to their arrangement regarding her tuition, is cold and distant to Emily. When Richard tries to make this Lorelai's problem, telling her she needs to 'straighten out' Rory because 'she's her mother and should set an example,' Lorelai's response is to shut it down with "I did set an example. I didn't go. Darn kids, can't teach 'em anything."
A Year in the Life Revival
Meta example: Netflix announced that it has reached a deal with the WB to release a limited series after a 8 year hiatus.
Luke, in his exhaustion and delirium over Lorelai fleeing to California to figure herself out, is swamped with people in the diner because e accidentally gave out the real WiFi password. Jess, seeing how scarily quiet the diner and how overwhelmed Luke is, just yanks out the router and tosses it to Luke as he leaves, kicking out the moochers in the process.
Jess: You didn't give me that password for six months and I lived here.
Lorelai goes out to California to hike, fails to do so, returns to the nearest coffee place to get coffee, can't get any, and then, confronted with the vista that is rural California, at last phones her mom with a story about how great her dad could be.
Emily's Character Development. She has to struggle with her husband's death, but not only she finds her way out, but she radically changes her life, seeking a career for her personal satisfaction, ditches her snobby socialite friends and takes her maid's entire family in her house. This last one is especially surprising as she had the nasty habit of firing one maid per week!