King Julien XIII supplies nearly ALL the moments of funny in the movies. The Penguins supply most of the rest.
In the first movie, he uses a skeletal human arm as a sceptre. While he's waving it around during the argument on the crashed plane, it constantly makes the appropriate positions as if it were his own hand.
The same thing applies when he is once again on the plane in the second movie, sitting on a skeleton's lap. Once again the skeletal hand makes the same motions as his own.
In the first movie the Penguins are called psychotic even by the other characters. They seem aware of this...
Gloria: Where are the people?
Skipper: We killed 'em and ate their livers. (Beat while we see Gloria's look of horror. Skipper just grins) Gotcha, didn't I?
The scene with the spider in the first movie.
I hear Tom Wolfe's speaking at Lincoln Center. [Phil signs frantically] Well, of course we're going to throw poo at him!
"If you have poo, fling it now."
In the first movie, the animals wash up on the titular country and are reunited. As Alex and Marty are reunited, in slow motion, there's this exchange:
A bit of Mood Whiplash during the Sad Times Montage, Alex falls down a cliff, landing on uncomfortable objects during the fall. Suddenly, he lands on a field of flowers...and then he falls into a field of cacti. The fall finishes with him landing into a river...which promptly leads him to a waterfall.
Also when Marty, Gloria and Melman are trekking through the jungles, they see some pretty scary creatures. They suddenly come across a cute little duckling...only for it to be eaten by a large crocodile. All three are visibly traumatized.
When the animals are riding the subway, a frightened man is sitting next to Alex on the seat. What he hears is an angry roar, what we hear is "Aw, Knicks lost again!".
Escape 2 Africa
In the second movie, King Julien is the first to suggest a volcanic sacrifice with a long and complicated argument with himself. Finally he finishes with:
Julien: Quickly! Before we all come to our senses!
Other Julien lines include:
Julien:(to Private, hanging from the light-fixture) You, in-flight slave... Bring me my nuts on a silver platter.
Julien: If I, King Julien (that's my name), only had two days to live, I would do all the things I have ever dreamed of doing. I would love to become a professional whistler. I'm pretty amazing at it now, but I wanna get, like, even better. (Makes fart sounds, spits attempting to whistle) And you know what else I would do? I would invade a neighboring country and impose my own ideology on them, even if they didn't want it!
One has difficulty imagining anything Julien had ever dreamt of doing that he had not done.
The launch, flight and crash of the 'plane' is a twenty-minute long moment of funny. Possibly because the penguins feature heavily in it.
"Place the bag over your face to hide your terrified expression from the other passengers."
The entire "Pass it on" scene in the second movie.
In the second movie, the fight between Alex and Nana (the old lady from the first movie), and towards the end of the second movie, the No-Holds-Barred Beatdown Nana gives Makunga when she sees him with her tote.
Just before that there's Alex giving Makunga said tote. This is funnier if you imagine it in Alec Baldwin's manly, sinister voice.
"Does the strap adjust? It does... yes I imagine this will be perfect for me when I'm out jogging."
When the Penguins steal the first jeep, they smash Nana through the windshield and leave her behind. Private asks, "Is she dead?" Skipper shouts out, "No!" and Kowalski promptly reverses straight into her.
Nana: "Ohh... that was beautiful... Now let's eat!"
Europe's Most Wanted
Just as the plane flight of the second movie was a long Crowning Moment, so is the Car Escape from the third movie.
Everyone looks on in horror as their van falls off a building with King Julien still inside... and a hopeful smile creeps onto Maurice's face.
Becomes funnier as he comes back up with the penguins' chopper, and while Mort is delighted, Maurice's smile fades.
Vitaly comparing Alex to a lioness with a beehive.
Julien stealing the Pope's ring as an engagement ring for Sonya.
And then immediately selling it to a motorcycle dealer. Sonya roars out of the shop, riding a brand new silver Ducati... right before the police aim their guns at the hapless motorcycle dealer.
Skipper revealing he spent the last of their money on gold teeth so he can eat apples... only to find out that he doesn't really like them.
On a related note, when he wants to buy an airbus made of solid gold, Kowalski points out that such a plane would fall from the sky. Skipper's response? "We'll be rich, Kowalski! The laws of physicswon't apply to us!"
Marty's "Afro Circus" song may be annoying, but it's so ridiculous it just builds the laughter out of you.
As Alex and Gia practice his made-up trapeze act, she follows every move he makes, which includes flying face-first into a pole. And catching onto the platform with their teeth.
When Julien brings the news that the other Zoosters have been captured by DuBois, Gia wants to rescue them because "circus folk stick together". The horses remind them all that the Zoosters lied to them, that they aren't really circus folk and don't belong. Vitaly's response is a hilarious literal Getting Crap Past the Radar that is also heartwarming and awesome:
Julien referring to Sonya as 'his hairy queen' was absolutely hilarious. As is most of his dialogue.
The scene where Julien, Maurice and Mort go into Sonya's train car and meet her for the first time. Cue creepy 'na na na' music in the voice of a child. The effect is reasonably creepy until the camera pans to Mort, showing that he was the one singing it.
DuBois: When in Rome...VIVE LA FRANCE!
(steals a police motorcycle)
Skipper: I hope you know what you're doing. You're risking Private's community college fund.
Private: (coloring a book) I'll never be president!
It's a fairly minor one but Alex and Marty argue over who should be the leader of their group early on in the film. This issue comes and goes up until they meet Vitaly for the first time and he threateningly demands to speak to their leader. Cue Marty using an exaggerated gesture to point to Alex as their leader. Alex's eye-roll is understandably funny.
"Deploy warp speed!"
The circus dogs. One particular moment:
Alex: Circus is in here.
(points to one dog's heart, and he looks inside his dress; another dog looks in there)