Axel trying and epically failing to give inspirational speeches. It gets to the point where Xion actually cuts him off with, "Yeah, we got your hokey speech memorized, Axel."
When Axel informs Roxas of what he intends to do for his vacation day.
You can equip joke weapons for all of the playable Organization XIII members. All of them are quite amusing, but the most hilarious one is Saix's, which is a GIANT. BANANA. His Limit Break can also be hilarious. Instead of mashing A, hold it down.
"Roxas, that's a stick."
Lexaeus taking Roxas into the tutorial on how to use Limit Breaks and literally punching Roxas into critical health so the player can practice. His matter-of-fact dialogue is what makes it; the gameplay models somehow manage to make it funnier.
Lexaeus: [A Limit Break] is the most powerful move at your disposal - one that only works when you are on your last legs.
"Do you always have to stare at me like I just drowned your goldfish?" Magnificent Bastard indeed.
The Organization is having a meeting discussing why Xion went rogue. Saix mentions that no one ever reported such a thing happening before, and Axel gets an uncomfortable look on his face. Saix clearly wants to say, "Axel, is there something you neglected to tell us about?" Unlike most moments, this one is funny on account of being awkward.
Said scene also contains one of the best instances of Voice Grunting in the game: the scene opens up with everyone sitting in Where Nothing Gathers, with the world's usual somber background music playing... and then the silence is broken by a Big "WHAT?!" from Demyx.
The entire cutscene when Roxas asks Axel what love is.
Roxas and Xion feel a bit awkward, internally, about keeping their identities a secret to the Genie.
On the 11th day, Saix tells Roxas that he'll be working with Larxene today. Roxas says "Right. Larxene. Umm..." and looks around the room for her. No-one's there, except for them two and Xigbar... who looks up and gives off an "Is this about me?" look.
Larxene telling Roxas to leave her alone and literally suggesting that he goes and hits his head against the wall.
"The only thing you could ever save me from is boredom."
From the 1.5 remix: Roxas scaring Axel on the clock tower.
In Roxas's journal, he notes that Axel told him that the ice cream was the "icing on the cake", but there was no cake, only the ice cream.
This one is really only amusing if you play Ace Attorney, but when investigating The Usual Spot (called Under the Tracks in Days) in Mission 23 (when searching for the missing Xion), you can examine the stepladder in the corner, which Roxas (somewhat surprisingly) refers to accordingly as a stepladder.
Report: "Name: Demyx ~ Place: A bunch of different places ~ Objective: Recon and stuff ~ Results: There was a bunch of stuff. And Heartless." Saix: A dusk could have done a better job. Rewrite it!
The discussion of Roxas having "pushed the wrong buttons" with Xion. In the manga, he discusses it with Demyx just as he's coming out of the shower. Demyx wonders to himself if they're good enough friends to talk with each other about stuff like that, and then gives Larxene as an example of a girl who was covered with wrong buttons because everything he said to her seemed to be wrong. He would apologize to her, not knowing exactly what for, only to be told by her not to apologize if he didn't know what he was apologizing for. Later, Roxas writes a letter to Xion that says "Sorry for pushing your buttons," complete with pictures of buttons that look like the ones on a PlayStation controller. And then there's Axel's look when he shows the letter to him.
On the first vacation day, the reader is treated to a page showing off how the other Organization members are spending their time. Many are doing predictable activities (i.e. Demyx is playing his sitar, Luxord is playing solitaire), but Xaldin is getting his hair done by a Dusk while Xemnas is just staring at Kingdom Hearts dramatically.
After helping Xion escape, Riku is ambushed by six members of the Organization, and winds up surrounded. How does he escape? He tricks four of them into attacking each other. The way Luxord is provoked has to be the crowning moment here.
Luxord: According to the cards— (cards are cut by Xaldin's lance) Oh, it's on!
Xion's reaction to Pluto tackling her out of nowhere.