Larry Gelbart or someone else associated with the show mentioned the episode in which the characters were being interviewed for a stateside news program. Father Mulcahy mentions to the interviewer that sometimes when it’s extremely cold, the surgeon will, upon cutting open a patient for surgery, warm himself by the heat rising from the patient. Supposedly they were told that as fact by someone who worked at a real MASH unit in Korea or Vietnam.
My nomination for Buffy would be the scene where Giles throws the book down in disgust, finally having translated the caption below the picture of the demon they’ve just finished fighting:
“It says, ‘Actual size.’”
It’s a great blend of the world-weariness that underlies much of the show along with the comedy and the unexpected turns things in the Buffyverse often take.
Star Trek TOS-The Edith Keeler speech
There might be a few better ones from the show. But it doesn’t get much more meta then Jerry and George explaining the basic premise of Seinfeld
ETA, here’s that Firefly clip. I always liked that scene and I’ll agree it pretty well explains Mal’s attitude and how he governs the ship. Like people used to say about Tony Soprano ‘of the bad guys, he’s the good guy’. Of course, that doesn’t completely apply here.
Same scene I was going to post. Up to that scene, you didn’t really know where the series was going. But it defined the entire series.
The final episode of the first season of Cheers!, when Sam and Diane are having their shouting match. He flings open the office door to throw her out, and everybody in the bar is on the other side, listening to every word. My all-time favorite moment!
My all-time favorite episode: when Coach’s daughter comes to visit early in the first season. I get all choked up every time I watch it.
Always Sunny: Dee and Charlie have been fired from not-working at the bar. They get hired at a TGIFriday’s kind of place, where the Waitress is a manager. Waitress tells Dee to fill the salt shakers, roll silverware, sidework basically. Dee: “Ooo, that sounds like a whole thing; I’m just gonna have a beer.”
Doesn’t include the entire cast, of course, but that’s how they all are. Beer is always preferable to anything resembling work.
Band of Brothers: It’s not a scene from the series, but the small story related by the real life Capt. Winters about his granddaughter asking him “Were you a hero, Grandpa?” His reply: “No, but I served with a lot of them.”
Six Feet Under: in the first season, Nate tells a client something like “We all die; you’re a ticking clock and so am I. Have you spent your time wisely?”
Doctor Who: The first clip in this video Defines the show, I think.
Big Bang Theory: Penny gives Sheldon a used napkin for Christmas.
I think for Twin Peaks it as to be the very start…
Pete Martell: Oh dear. Lucy? Lucy, this is Pete Martell. Lucy, put Harry on the horn.
Lucy Morgan: Sheriff, it’s Pete Martell up at the mill. Uh, I’m going to transfer it to the phone on the table by the red chair. The red chair against the wall. The little table with lamp on it. The lamp we moved from the corner? The black phone, not the brown phone.
Sheriff Truman: Morning, Pete. Harry.
**Pete Martell: **She’s dead, wrapped in plastic.
For Supernatural, I think it’s the scene where the brothersdiscover their fan base.
Fourth wall? What’s that?
Roseanne: They get a notice that their electricity will be shut off for non-payment. Roseanne is trying to turn up the freezer just as the lights go out so she closes the door and says with a smile, “Well, Middle Class was fun.”
That is good…
…but this is better. 
“No. We have to stay here, and there’s a simple reason why: ask ten different scientists about the environment, population control, genetics, and you’ll get ten different answers. But there’s one thing every scientist on the planet agrees on. Whether it happens in a hundred years or a thousand years or a million years, eventually our sun will grow cold and go out. When that happens it won’t just take us. It’ll take Marilyn Monroe. And Lao Tzu, Einstein, Marobuto and Buddy Holly and Aristophanes. All of this, -all of this-, was for nothing. Unless we go to the stars.”
From Babylon 5.
For x-files, by far its that episode where they bring in a new agent who represented legions of fans.
Pawn stars: the episode where chum lee fixed the secret Santa. Usually, they’re assholes to each other, but that episode showed how much they really cared about each other.
Married with children: similar to above, where they try to commit insurance fraud after they think their car is stolen. After they recover it al says the trunk contains his most valued possession. He pulls out a copy of Jugs magazine, which actually has a picture of his family in it. Really hit the nail on the head about what that show was all about.
Seinfeld: tons of choices here, but im going with the scene in The Bet where Kramer comes in and throws the money on the table. It shows the essence of a show about nothing, yet highlighted all the characters inherent selfishness.
Happy days: the opening sequence where the fonz is about to comb his hair and then realizes its already perfect. to many people the 50s will forever remain perfect in their memories, just like the fonz’ hair.
Newhart: The Finale.
B-5 was my favorite show ever, and reading this thread has had me trying to think of what I thought the defining moment was.
I don’t have to think about it any more, you nailed it.