(after a lengthy discussion of his diseases balancing one another out)
Mr. Burns: So what you’re saying is, I’m indestructible.
Doctor: Oh, no, no, in fact, even slight breeze could…
Mr. Burns: Indestructible.
Burns gets Chinese take-out:
Burns: [counting out change] That’s ninety-six, ninety-seven, ninety-eight–ah, thirteen dollars and ninety-nine cents.
Delivery Man: Sir, tipping IS customary.
Burns: Oh, me no speakee Chinee!
Look at me, I’m Davey Crocket!!
Burns:That’s right, keep eating, little do you know you’re drawing every closer to the poison donut. There is a poison donut, isn’t there Smithers?
Smithers:Actually, sir, I discussed it with our lawyers, and they consider it murder
Burns: Damn their oily hides!
Burns:“I call it the Spruce Moose! It can carry 400 people from New York’s Idlewile airport to the Belgian congo in 17 and a half minutes.”
Smithers:“Thats a nice model, sir”
Burns:“Model?”
Environmentalist Protester 1: All right! We’re finally going to stop those corporate pigs from dumping that nuclear waste!
Environmentalist Protester 2: Oh, no! Our boat is sinking!
Burns: It was I, you fools! The man you trusted wasn’t Wavy Gravy at all! [tosses a guitar away] And all this time, I’ve been smoking harmless tobacco!
Burns: Now, I want ti to be said that I despise you. You are the worst part of society, you live off of pain and misery and suffering! I’m sorry ,where are my manners, would anyone care for some coffee?
Lawyer: I’ll have some.
Burns: You want it black, don’t you! Black like you’re heart! I hate all of you!-I’m sorry, it’s my problem, I’ll deal with it.
Burns: I don’t know what ‘phallocentric’ means, but no girls!
From the “X-Files” episode:
Burns: “Now that I’ve regained my senses, I do NOT bring you love and joy! I bring you fear and pain and…”
Dr. Nick: “Time for your booster Shot!”
(Injects Burns)
Burns: “Ah! Good morning Staaarshiiiiiiiiine. The Earth says hellooooooo…”
Post #23.
I don’t think Monty Burns ever said that.
Although it is pretty funny to imagine Burns saying it. “Post number twenty … three.” 
“Do as I say!”
(Filling out his social security number)
“ought-ought-ought, ought-ought, ought-ought-ought, two.”
“The telephone is so impersonal. I much prefer the hands-on touch you can only get with hired goons.”
After reading Homer’s insulting letter to him, and hence plotting his revenge:
Burns: I could crush him like an ant, but that would be too easy. Instead I’ll bide my time, slowly turning the screws on him like…ahhh, the hell with it. I’ll just crush him like an ant."
“Damn Roosevelt!”
[And it was “naught.”]
(talking about one of his attack dogs): I’ll never forget the day he bagged his first hippie. That young man didn’t think it was too “groo-vy”
The line itself isn’t all that funny…but the way he says “Groo-vy” kills me (like the aforementioned “give the men their tar-tar sauce” line)
Burns: I thought I’d chauffeur myself this evening. Yes, that’s what I thought. How difficult could it be? I’m sure the manual will indicate which lever is the velocitator and which the deceleratrix, hmm?
Burns: Out of my way. I’m a motorist!
Burns: His breath reeked of beer and pretzeled bread.
Burns: Smithers, this beer isn’t working. I don’t feel any younger or funkier.
Smithers: I’ll switch to the tablespoon, sir.
And, of course, funnier every time he says it.
Burns: Simpson, eh?
But Monty does then say upon snapping out of the flashback, “Ah, if only we had listened to that man… Instead of walling him up in the abandoned coke factory.”
Or, in a non-verbal reference, the picture of the front page of the newspaper:
BURNS BIRTHDAY TODAY
Credits Long Life To Satan
[picture of Burns and “that goat-legged fellow” with a giant check for $1MM]
Burns: I’ll have my lunch now… A single pillow of shredded wheat, some steamed toast, and a dodo egg.
Homer: But, I think the dodo went extinct…
Burns: Get going! And answer those phones, install a computer system, and rotate my office so the window faces the hills!
Simpson, Simpson… … French, is it?
Also important was the dog’s name: Adolf.