I simply loved the boring child who told all these very uninteresting stories. Vernon, maybe?
He was hilarious.

While not a hilarious moment, Milla's party has to be the best level in terms of fun.
As for hilarity, I'd agree with the guys who loved the Milkman spies and the Bonaparte level.
Specifically:
Street worker: Look at that woman's breasts. They're large.
Grieving Widow: I hope he left me as the sole beneficiary of his 401K plan
The knight that will go to war only if he eats snails.
Liked Lilly and the old man too.

I found it! ;P Played the level today and had great fun.

Especially laughed at the end after defeating the boss. When you go to his body and talk to him, Raz comments "He may have been evil, but he has build a lot of roads for this little city..." which sure is a reference to old (german) people arguing that "Hitler wasn't so bad, after all he built the 'Autobahn'!"... :P

Yes the artwork was fantastic, and in terms of the psychological character descriptions, that was one of the most interesting.

and of course the painting-selling dogs! they were hilarious :D

When you first discover that Dogen's brain has been stolen and you keep trying to tell everyone.

Everyone replies with "No, he's just like that" :D

Again, I'll have to go with The Milkman Conspiracy and the stuff the agents would say.
Widow: There are dead people under the ground. I have brought flowers for them because I am sad.
Gardener: Plants need to be given water, because they cannot drink out of a glass.
Sewer worker: I often smell of excrement, but I deserve respect because I provide a valuable service.

I loved agent Cruller and some of the dialogue with him. When he discovers all the children had their brains removed, he asks you to become his secrent agent. The dialogue that follows is hilarious:
Agent Cruller: Are you ready to be my secret agent?
Raz: No, not yet.
*Agent Cruller slaps Raz in the face*
Agent Cruller: How about now?

For some reason, I love Cruller merchant saying, "The Big headed kid with the gloves!"

Which, incidentally, I can mimic near-perfectly.

The baking housewives in the Milkman's level say:
"Although over time my husband will lose desire for me sexually, he will always love my pies. "

Cannot lurk forever, bear

I found Clairvoyance to be one of the most hilarious things about the game. Seeing how everyone perceives Raz is just brilliant.

Gloria- picture of herself, waiting to be autographed
Bobby Zilch- punching bag with a target on it
Sasha Nein- miniature Sasha
Sheegor- the Messiah with goggles
the dogs in the theater- fire hydrant
Vernon with the boring stories- a giant ear

Just epic.

Mikhail's Half-deadly Nelson speech.



"Are you the real Napoleon Bonaparte? I mean the imaginary real Napoleon Bonaparte?"

Bacon!

And the entirety of Black Velvetopia. Knocks me out every time that I play through it.

Vernon's longest walk ever! :D

"TEE-VEE"!

I'm partial to the cutscene you unlock for reaching psy rank 100, though that's not a task for the faint of heart.
Mr. Pokeylope is the man.

Some of my favorite moments:

The entirety of The Milkman Conspiracy, but the part that made me laugh the most was when Raz says to Boyd "Your name's no longer Boyd, it's 'Roid because you're such a pain in my butt!"

From Sasha's Shooting Gallery:
Sasha: Now, say something hideous jumps out at you, something so horrible it must be destroyed. [he makes a colorful lamp appear] Ugh, it's so tacky! I can't look directly at it! But, I control those feelings, concentrate, and...release! [he destroys it] And the world is a better place.

From the intro:
Raz: My name...
Oleander: Starts with a D...
Raz: ...Is Razputin.
Dogen: PLEASE DON'T EAT US, LAKE MONSTER!!!

From the tutorial level:
Sailor kid: CHARGE!!!
[he gets blown up by a mine]
Raz: Hey! Why did you kill that kid?
Oleander: I didn't kill him, he just got his astral projection kicked out of here. And I'm gonna kick your ASS-tral projection out of here too if you don't get moving!

From the "Let's Make Out!" cutscene:
Lili: Oh no, you didn't just hit my boyfriend!

All of the news reports in Lungfishopolis (and the whole Lungfishopolis level in general)

All of the wrestling matches in Black Velvetopia, and the dialogue in them.