The Triceraton invasion gives us a few, not least:
"Hey! That's the Prime Leader's ship. Didn't we steal this once before?"
"And guess what? We're stealing it again."
Followed immediately by...
"Prime Leader! The, uh...the...the terrapin creatures have stolen your private space cruiser." (beat) "Again."
"WHAT? I just had it detailed!"
Earlier on, when Casey and April are organizing the human prisoners:
Casey: Alright people, listen up! No acting like people in an invasion movie, 'cuz they always get vaporized! Somebody always gets vaporized. Yo pal! It's probably going to be you! It's like you got a sign on your back that says 'Vaporize Me'!"(the other people back away from the guy he's pointing to.)
The turtles unknowingly befriending Hun online while playing an MMORPG.
The Reveal that the Ultimate Gamer was just a little girl.
An understated one comes from the 'Rogue in the House' arc, after Don encounters Stockman— or, rather what's left of him. Stockman tries to charge at him from within the jar... and Don jumps backwards, like he had some reason to worry. Aside from the The Smart Guys proving that they're Not so Above It All, the squeak that Stockman makes as he collides with the jar may be what makes the scene.
Raphael's reaction to Bishop's "aliens" attacking.
Mikey has been shirking his training (and bragging about being the Battle Nexus Champion)... right when Kluh challenges him to a rematch. He freaks out and tries to get the others to help him train, resulting in:
Mikey:"Master Splinter! You'll help me, right? You'll train me?"
Splinter:"Training, Michelangelo? Surely there are comic books I could be reading, or perhaps I could go watch television instead. Ah, wait my son, I know! Perhaps instead of training, I will go eat pizza! Yes, pizza sounds very appetizing right now. With pepperoni! And karma!"
Mikey brings up being the Battle Nexus Champion for the umpteenth time, prompting one of the other turtles to comment that he's surprised that Mikey doesn't wear the trophy around his neck. He replies that he tried to, but the chain kept breaking.
The Shredder ends up allying with the Turtles to stop Stockman during "Return to New York, Part III". But every time they seem to succeed, Stockman just comes back.
Leo: What do we have to do to stop this guy?!?
(exasperatedly) Shredder: I have asked myself that question many times...
In "The Shredder Strikes Back, Part One," during one of the scenes of the Turtles hanging out in April's apartment, we get this exchange while Raph and Donatello are watching TV:
Mikey: (Steps in front of the TV) May I have your attention please.
Everyone looks at him. He proceeds to cut loose with an extended belch. Raph and Donatello applaud him. At a nearby table, April looks disgusted. Splinter looks somewhere between resigned and amused.
Splinter: (To April) This is what I live with all the time.
Don: Say what you will about the Foot, they do not skimp on the headgear.
Also from "The Shredder Strikes Back, Part Two," we get the following one-liner from Mikey when the gang finds an avenue of escape:
Mikey: Ladies and gentlemen, turtles and rats, run, do not walk, to the nearest exit!
For all the drama and intense fighting of "The Shredder Strikes Back, Part Two," it does have quite a few funny moments. When the Turtles retreat to a walk-in refrigerator, things go quiet. Mikey wonders if the Foot ninjas retreated, leading to the following exchange:
Mikey: Kinda quiet out there...you think they all just went home?
Also, Raph taunts the Shredder, who latches onto his head in response;
Mikey: Get it off! Or there's gonna be a tiny little Shredder alien busting out of Raph's chest! (Gets Dope Slapped) Ow!
The way Casey Jones screws up his attempt at proposing to April O'Neil.
Casey: I love you as much as Gretzky loves hockey, April, and I want to play you for the rest of my life. I mean, the rest of your life! I mean, Gretzky's life!
When someone attempts to assassinate Leonardo during the Battle Nexus tournament, he uses a makeshift weapon. The makeshift weapon in question? What appears to be The Shredder's helmet. The implications of it and Leo throwing it away in disgust are amusing.
In "Notes From The Underground part 2" while the group is following Quarry off a cliff into a whirlpool:
Don: Following monsters off a cliff may not be the smartest thing we've ever done.
Mikey No, but it's definitely the grossest, that thing looks like a gigantic toilet!
During one of the episodes in the first season after rescuing Angel with Casey and returning her to her grandmother who offers him a slice of pie in gratitude, Mikey wants some. But his brothers drag him off telling him they are ninjas and they live by the shadows never to be seen.
Don: Getting the Golden Puck back feels more like something for the police to handle.
Leo: Maybe, but Casey could get hurt.
Raph: Or worse, Casey might hurt somebody.
Mikey: Where's the pie? I distinctly heard the word "pie".
The Incredible Shrinking Sterling has a priceless moment when Sterling is lost in time and lands in the sewers and thinks he's back in the present only to see the toddler turtles mistake him for a toy.
Sterling: Oh, yuck! The sewers...Oh well, at least I've arrived back to present day.
Don: Hey, check it out!
Mikey: Cool, a toy!
Sterling: Or maybe not!
"The Battle Nexus, Part Three": Raph's total freak out when Mikey beats him.
A small moment, during the episode "H.A.T.E. when Donatello and Raphael search the titular group's base for bombs the high pitched fear squeak Donny makes when he sees the bomb in question is both hilarious and ADORABLE
Speaking of "H.A.T.E.", Casey's mom has the best ending line:
Casey's Mom: One more thing: you don't have to tell me now, but someday I'd really like to hear the story behind that big rat and the giant turtle.
Any time in the show when they make fun of the original cartoon.
"Secret Origins Part 3" has a particularly funny bit where April wears a yellow jumpsuit to try and disguise herself as a news reporter. When questioned about it at the end, she responds with, "Yeah, in another lifetime maybe."