Base-Breaking Character: Doris. Deliberate heartbreaker, or a flawed character whose fickle nature has her making the same mistakes over and over, but still likeable enough?
Bellisario's Maxim: The penguins can't read and need to consult Phil and Mason to read for them. Except for all the times when they clearly can read when it's important for a joke.
Big Lipped Alligator Moment: Subverted in "Eclipsed." King Julien gets a big, long musical number about his "congaga." Although this musical number has all the trappings of a BLAM in its over-the-top, out-of-nowhere-ness (keep in mind the show almost never does musical numbers), it sets up the plot.
Cargo Ship: Julien flirted with both Rico's Miss Perky doll and a fruit smoothie in "Hello Dollface" and had some slight narcissistic Ho Yay with the robot version of himself in "Lemur See, Lemur Do", and Kowalski had a thing for the animal control officer's van.
All the songs in Return of the Revenge of Dr Blowhole.
Fandom Rivalry: When "In the Happy Little Land of Hoboken Surprise" took the Emmy Award for Best Original Song, the Brony community wasn't pleased as it won against two of FIM's songs.
"Funny Aneurysm" Moment: All the jokes in "The Hoboken Surprise" about Hoboken being a terrible place are a lot less amusing after Hurricane Sandy. Or Hurricane Irene, for that matter (the episode literally aired a week before the latter storm hit).
Hans mentioned that he kissed Skipper's sister but Skipper claimed that he doesn't have a sister. Given the similarities Skipper has with Clover, one would wonder what would Skipper say if he met her◊.
Ho Yay Shipping: And how. There's an awful lot of subtext between Kowalski and Rico, and they're just the most obvious...
Jerkass Woobie: One episode features a poison dart frog with such potent venom that the merest touch renders one temporarily paralytic and with a comical rash; he uses this power to keep all the other animals at his pettiest whim. Private eventually realizes the real root of the problem-a Freudian Excuse. So he knocks up a protective suit that will allow him to give the slimy little chap a hug. Nearly subverted, until it's pointed out that the line between "hug" and "Let's see how far your eyeballs will fly" is a thin one indeed.
Officer X. His antagonism toward the penguins is because they thwarted him in the process of doing his job.(In their defense, they WERE protecting someone they considered a friend) While you can't blame the penguins for trying to keep themselves safe, anytime he's not opposing the penguins, he's really just doing his job, and his "reward" for this is constant public humiliation and scorn.
King Julien, hands down. Not only do fans pair him up with Mort and Maurice, but every single penguin too. The show provides plenty of examples and has even paired him with Marlene and Rico at various times. It's only a matter of time before they pair him with himself.
As the closest thing the show has to a female lead, Marlene gets a lot of play as this, though pairing her off with Skipper is by far and away the most popular.
Fans pair up Skipper and Marlene based on the fact that the two spend so much time together. There are 80+ fanfics about this couple alone.
Just about anyone can be shipped to anyone else; as mentioned above, King Julien gets shipped with just about everyone, and the penguins with each other. Of course, the healthy doses of Ho Yay and Ship Tease help.
Squick: In Friend-in-a-Box, Julien happily tells Kowalski that he never learned the Potty Dance, because as king he's entitled to go wherever he happens to be at the time. Kowalski backs away from him with a disturbed look.