After escaping a hot-air balloon which took him out to a sea storm, Rocky is flying back to the shore, where he is mistaken for an enemy plane and shot at with flak cannons. In order to prove he isn't an enemy, Rocky flies in a certain pattern to spell out two words. Upon reading them, the general in charge of the air defences orders them to cease fire immediately. The words which Rocky spells out: US Taxpayer.
The boat race between Rocky, Bullwinkle, Boris and Natasha, which goes from the lake in Frostbite Falls to smaller and smaller bodies of water, including puddles and irrigation creeks, all while Boris instructs Natasha to keep rowing and Bullwinkle keeps pouring water out of a bucket to contain a leak in his boat, actually a downed airplane.
Boris: Stroke stroke stroke!
Bullwinkle: Bail bail bail!
In another episode, Rocky and Bullwinkle are inside of an airplane falling out of the sky (surprisingly, this isn't the first time this has happened to them.) Instead of jumping out, they decide to find a way to keep the airplane afloat. Rocky comes up with the brilliant idea of using hot air, but where are they going to find the hot air they need? Rocky pulls out a copy of the US Congressional Record and tells Bullwinkle to start reading from it.
For those of you not in the know, the Congressional Record can be revised to correct "errors" by the politicians themselves. The "fixes" that can be implemented can be as egregious as adding whole new speeches or removing those in which the politician shot himself in the foot.
The government suffers another shot in the Goof Gas arc, when Boris and Natasha attend a congressional hearing. After the speaker has finished talking gubernatorial nonsense (Specifically, a statement that the government needs to remove the government from the process of running the government):
Natasha: Boris, what he said! You think he's already had Goof Gas?
Boris: Natasha, what he said, that is Goof Gas!
The reveal that Mr. Big is in fact smaller than Rocky.
The show's first real meta gag: after the mooseberry bush dies and Bullwinkle makes off with the mooseberries, only for them to (seemingly) explode and take Bullwinkle out with them, Natasha laments: "thirteen episodes worth of effort, wasted!"
The show has mocked itself several times despite its popularity. Below this paragraph is probably the most famous one from "The Treasure of Monte Zoom": What Rocky & Bullwinkle say after Boris & Natasha decide to use an A-bomb to open the chest.
Rocky: They said "A-bomb." Do you know what that means, Bullwinkle?
If we can put Fractured Fairy Tales here (since there seems to be no page for their funny moments), the entire "Riding Hoods Anonymous" episode is comedy gold. Especially the running joke about the basket full of (BOOM!) ...goodies.
The episode where Natasha tells Boris to "Sharrup your mouth!"
This from "Lazy Jay Ranch", when the pair finds out exactly what kind of ranch it is:
Narrator: Good heavens, both of our heroes have fainted! What did you tell them?
Lazy Jay: Just told them what we raise on this ranch.
Narrator: Well, what is it?
Lazy Jay: I better whisper. (to the camera) Worms.
Narrator: WORMS?!?! (faints)
Lazy Jay: Well, I'll be doc. He fainted, too.
Near the end of one segment, the Narrator is too busy laughing at one of his own corny jokes ("Tune in for our next arrowing episode...") to finish the outro, and an un-amused Rocky and Bullwinkle have to do it for him.
This conversation between Rocky and Bullwinkle in "Goof Gas Attack".
Bullwinkle: You'd better, we could use the publicity...
Also in "Goof Gas Attack": "We'll declare war on EVERYBODY, but we won't tell ANYBODY!"
"It's... Time for Ding-Dong School!"
In the Mr. Peabody segment "Mati Hari", Peabody makes a pun and Sherman says that he should have saved that for the ending, to which Peabody remarks "I've got one much worse than that". At the end, Sherman groans at Mr. Peabody's ending pun, and Peabody says, "I warned you Sherman".
In the "Ruby Yacht" story arc, Rocky and Bullwinkle go to a library to research the ruby, and the librarian complains about that "noisy cat, always stomping around". The cat in question isn't making any noise.
An instance where the delivery kills it.
Bullwinkle: The rules clearly stipulate no human over ten can participate. I'm about as inhuman as you can get.
Rocky: You're a moose!
Bullwinkle: And that's another reason!
In the "Wossamotta U" arc, Natasha finds out Boris went to "college":
Natasha: Boris, you went to Penn State? Boris: No, state pen.
The Poetry Corner segment, where Bullwinkle attempts to recite the works of a certain Marshall Mathers the Third. He makes it through a few lines of Superman before stumbling across Eminem's trademark foul mouth in the book he was reciting from. He then flips through the rest of said book to find something less offensive to read from...then inevitably has to cut the rest of the segment short.
On the DVD, the outtakes of the last part of the "Goof Gas Attack" storyline, especially hearing the cast laugh everytime Paul Frees tries to say Peachfuzz's line, "Heavens to Eliza! He's a little fuzzy comet!"