From the first film, when some hooligans leave a bunch of beer bottles on Miyagi's truck. They refuse to leave, so Miyagi chops the bottles in half with one swing, terrifying them away. When Daniel asks how he did that, Miyagi replies "Don't know. First time trying."
After they arrive in Okinawa in the second film, and see a poster of Sato breaking a log with his bare hand, Daniel asks Miyagi if he could do that. Miyagi snarks, "Don't know. Never been attacked by tree." This then becomes a Brick Joke as he smashes a huge tree trunk with one blow during the storm.
Miyagi: No! Not bow! (points to the front of the boat) BOW!
When Miyagi requests the Cobra Kai leave Daniel alone to train for the All-Valley Karate Championships:
Kreese: All right, no one touches the primadonna until the tournament. Is that understood?
In the first film, the Cobras and Daniel have a truce established until the tournament. However, Daniel attempts to stick it to the Cobras by asking a teacher to repeat for them what is implied to be a dry, boring lecture. This backfires when the Cobras all promptly scatter away to class, leaving Daniel to listen to it alone.
Miyagi finally gives Daniel some offense training and uses himself as a target.
Miyagi: Now punch hard. Hya! (Daniel punches him) What's the matter, you some kind of girl or something? Punch! Drive a punch! Not just arm! Whole body! Hip, leg, drive a punch! Make kiai! Hya! Hya! Give you power! Now try punch! Yosh!
Miyagi: Punch some more! Yosh!
Miyagi: Punch some more! Yosh!
Miyagi: Very good, Daniel-san! Yosh!
Daniel:(punches) Hya! Hey, pretty good, huh? Hya! (punches again while moving around)
Miyagi: Hey, oi, oi...
Daniel:(moves around and punches) Look at this, Mr. Miyagi! Hey hey hey! Hya!
Miyagi vs. Kreese is hilariously one-sided. After Miyagi shoves him off Johnny, Kreese punches, and Miyagi dodges, leading Kreese to punch through a car window. He spins around, goes after Miyagi again with the other hand...and the same thing happens. Miyagi then grabs Kreese and forces him to his knees, raising a hand above his head and speaking in a dead serious tone of voice:
Kreese's utterly dumbfounded expression, and the wink Miyagi gives Daniel afterwards, really sell it.
On the plane ride, Daniel is trying to find Tomi Village on the map, and constantly asking Mr. Miyagi questions about Okinawa. The poor guy just wants to get some sleep, but Daniel just doesn't get the hint. Finally, Miyagi tells him to look in the morning—maybe it'll be there then.
Miyagi has a short exchange with a woman in Tomi Village. He explains that he thinks they went to school together. He'd introduce her to Daniel, but he's forgotten her name.
Daniel asks what Miyagi would've done if Sato had thrown a punch at him. Miyagi's response? "Block."
When practicing the drum technique, Daniel is practicing with the hook and knocks himself into the harbor.
Miyagi: Daniel-san. Are you all right?
Daniel: Yeah, I'm sorry. That was pretty stupid.
Miyagi: (Gives him a "No, duh" look) Miyagi say that to father when same thing happened. Father agree he was stupid. (Beat) Father was right.
Then we get this:
Daniel: Hey, is there a counter-punch in the technique?
Miyagi: Ask drum.
When Daniel expresses worry about Miyagi being slandered:
Miyagi: Daniel-san, lie become truth only if person want to believe it.
Daniel: Is that another old Okinawan saying?
Miyagi: No, new Okinawa saying.
Daniel: How new?
Miyagi: About ten seconds.
Daniel is being pressured by Chozen to participate in a contest to break sheets of ice. Daniel keeps trying to back out, but Chozen won't let him. Miyagi arrives and says he'll take care of everything. Then he turns around and bets six hundred dollars Daniel can break all of them.
Sato's face as Daniel does the breathing technique. It's implied that he recognizes what's about to happen and is very clearly thinking, "Damn, I'm about to lose 1800 dollars!"
In the third film, when Silver tries to take on Miyagi, he starts making Funny Bruce Lee Noises at him. Once Miyagi finishes kicking his ass he waves his hands around in a goofy fashion and mockingly does the same. With a totally straight face.
After Julie manages her leaping kick, she dances around the garden cheering. Miyagi's face is a mix of pride at her accomplishment and embarrassment at her antics.
When she complains about not getting a belt, she points out that even Elvis Presley got a black beltnote He was a first dan in American Kenpo, as a matter of fact. Miyagi snarks that maybe she should borrow from him, then.
As he's teaching her "Wax On, Wax Off," he congratulates her...then notes that she missed a spot.
Miyagi and Julie discuss her upcoming prom in The Next Karate Kid:
Miyagi: You tell Eric we go to prom. Julie: What do you mean "we", Mr. Miyagi? Miyagi: Miyagi drive car. Julie: Mr. Miyagi, it doesn't really work that way. Miyagi: Then Mr. Miyagi stay at home and wait like anxious parent.
Then Eric shows up to a house full of visiting monks. He takes it in stride, but one can only imagine what he must be thinking. And as if that weren't enough, the poor guy ends up on the business end of Miyagi's Twerp Sweating... while Miyagi is holding a knife. (He's chopping vegetables).
Miyagi goes dress shopping on behalf of Julie, and finds that he has absolutely no clue what he's doing. Bullies? Fellow karate masters? Angry men with weapons? No problem. Going dress shopping for a girl? He's completely out of his depth.
Miyagi teaches Julie how to waltz...by practicing a kata.
Dugan announces that he's going to put Miyagi's lights out. After the fight, which goes about as well as you'd expect, Miyagi grabs him and pulls back his hand and speaks in a dead serious tone of voice, just like with the Kreese example above. "Time to put your lights out!" Then, instead of chopping, he just lets out a puff of air, like blowing out a candle, and lets Dugan collapse.
The final scene of the film has Julie being proud of beating up the Alpha Elite, while Mr. Miyagi reminds her that fighting is not good. Then...
Julie: Mr. Miyagi. Come on, admit it. We kicked some butt.
Miyagi: Julie-san. Fighting not good. But if must fight...win.
Not from the movies themselves, but Martin Kove starring in Intuit Quickbook commercials as John Kreese. A Lighter and Softer John Kreese who, thanks to Intuit Quickbook making running his dojo easier, has established Koala Kai, the antithesis to Cobra Kai. Made better because Kove's clearly having fun as a kinder, gentler version of his famous role.