"He spelled 'Yale' with a 6." "I'm not made of Airports"

Flanders: “Buenos-diddley-ding-dong-dias!”
Space Coyote, mildly frustrated: “Homer, you don’t even have a computer.”
Ralph Wiggam: “Mrs. Crabapple, I ate my worm.”
Mrs. Crabapple: “Just put your head on your desk and rest, Ralph.”
Apu: “AND GET OUT!!.. And come again!”
Class, watching Sex Ed film: “EEEEWWWwww!!”
Mrs. Crabapple, unimpressed: “She’s faking.”
Horse Trainer: “Despite my patrician facade, I assure you my heart is breaking.”
Rev. Lovejoy: “You have your Christians, your Jews, your…(looks at Apu)…Miscellanous…”
Apu: “Hindu! There’s 800 million of us, you know.”
Rev. Lovejoy: “That’s super.”
Homer, lovingly caressing the game ball: “I will call it ‘Stitchface.’”
Smooth French Guy, after Marge wildly throws her bowling ball across the lanes and smashes a hole in his lane: “Entirely my fault.”
Apu: “Please do not offer my god a peanut.”

“If it’s about laying off the insanity peppers, I’m way ahead of you.”

Barney, in his French art film: “Don’t cry for me, I’m already dead.”
Lisa: “I don’t see what the big deal is. He’s just a good looking rebel who plays by his own rules.”
Mr Burns: “I’ll sign that check when pigs fly.”

Later, we see Smithers and Mr Burns standing by a window and Homer’s BBQ pig goes flying past (long story)
Smithers: “…shall I… fill out that check, sir?”
Mr Burns: " I think not."

This is my sandbox. I’m not allowed to go in the deep end. That’s where I saw the elf. He told me to burn things.

Lisa: Dad, we did something very bad!
Homer: Did you wreck the car?
Bart: No.
Homer: Did you raise the dead?
Lisa: Yes.
Homer: But the car’s okay?
Bart & Lisa: Uh-huh.
Homer: All right then.

Lisa: Dad, what’s the point of this story?
Homer: I like stories

I know someone who actually used this in a speech once

Flanders: Feels like I’m wearin’ nothin’ at all! Nothin’ at all! Nothin’ at all!

Lisa: “Why do they call you ‘Bleeding Gums Murphy’?”
Bleeding Gums Murphy: “Ever been to a Dentist?”
Lisa: “Yea.”
Bleeding Gums Murphy: “Not me.”
Ok, I’m done.

Ralph: “Oh, boy, sleep! That’s where I’m a viking!”

Marge: “Homer, did you shut the gate?”
Homer, annoyed: “Yes.”

(The wind catches the gate, Slam! Slam!)

Marge: “Homer, I thought you said you shut the gate!”
Homer: :“OOhhh…, you mean* today*…”

(I can’t stop)

Homer, sitting in the cockpit of a commercial jet, fascinated by the console: “Hey, what’s this switch for?”

Pilot, quickly grabbing Homer’s hand: “We need that to live.”

I’m just going out…to stalk… Lenny & Carl

Skywriter: “I have to deliver a message. It’s the skywriters’ code!”
Homer: “I am so sick of that code!”

Skywriter: “You maniac! You’ll kill us all!”
Homer: “Correction: Kill us both!”

(Homer is frantically mashing the buttons on the phone in a vain attempt to navigate the overly-complex police/911 voice menus)

Voice menu: “You have selected…Regicide. If you the name of the king or queen being murdered, press “1”.”

…“know”…
D’oh!

“…and then the doctor said the worms were all gone, and that was the happiest day of my life.”

Trying is the first step towards failure

[Krusty]I used to be a big cheez… A huge cheez! Now I have to ride the bus, like an idiot. (…) Aaargh… This is no life for a clown.[/Krusty]

During parole hearings, it is pointed out that Sideshow Bob is wearing a shirt that says ‘Die Bart, Die’ - which he then claims is German for ‘The Bart, The’ (Die is female, though, that would have to be Der Bart, Der. Anyway). Upon hearing that, one of the ladies on the parole board says:

‘No one who speaks German could be an evil man’.

Marge is complaining about being treated like a chauffeur…

Homer: Now Marge, chauffers wear special uniforms. Keep this up and you’ll be in trouble with the delivery commission.
Marge: to HELL with the delivery commission!
Homer (shocked): Marge… you don’t know what you’re saying!
Homer: I’ve never lost a fight to an animal
Bart: You lost against the worms in our backyard.
Homer: That wasn’t a loss… it was a strategic withdrawal
Bart: Then how did they make you build that statue?
(Pan to statue of Homer grovelling before a giant earthworm. Plaque reads “WORMS ARE BETTER THAN ME”)

Nitpick: That’s “The Livery Commission”, not DElivery. I thought it was a fancy name for a Chauffeur’s union when I first heard it, but a little googling suggests it’s more like a local government standing committee on taxicab-related regulations:
Taxicab and Livery Commission of Lowell, MA

ETA: The worms bit isn’t actually familar to me - what episode was that from?

Viagra? I don’t know what that is, but it’s going in Skinner’s coffee.

You’ve conflated two separate (but very funny) situations.

Bart is trying desperately to get through the 911 jail-mail system so types in a crime code at random and gets the regicide message.

Homer, who has reached 300lb so he can be classed as obese and work from home, realises the plant is going to melt down and tries to use the phone to warn them of the danger they’re all in. However the phone isn’t equipped to deal with his chubby fingers so he gets this message:

“The fingers you have used to dial are to big. To order a dialing wand please mash the keypad with your fist now.”