The bit where Genie snaps his fingers and turns Abu into all kinds of different things, before settling on an elephant. He's not even looking at Abu, he's letting his mind wander, and that just makes him more human.
If you had to name a moment that doesn't include the Genie, it would be in the "One Jump Ahead" sequence, when Abu pulls a scimitar on the guards.
King of Thieves manages to top it, Call Back style.
Abu:*Throws sword up, cutting a chandelier's cord and dropping it on the thieves*
How about during the "Prince Ali" song, Jafar tries to keep the parade out of the palace only to get squashed by the door? How he and Iago look afterwards probably counts.
And then when the Sultan introduces him, joyfully telling "Ali" that Jafar is delighted to meet him too. Cut to Jafar standing with his arms crossed giving them a Death Glare, and then mutters "ecstatic" in the most deadpan voice possible.
The Sultan's joyride on Carpet, which includes him telling Jafar to "button up", buzzing Elephant!Abu, and Carpet ending up falling-down dizzy.
"You've heard of the golden rule, haven't you? Whoever has the gold makes the rules. HUUUUOOOOYYYYYEEEEE!!"
Aladdin's ploy to rescue Jasmine from the marketplace after she steals an apple. It becomes even funnier as Jasmine plays along with his insanity plea.
Aladdin: Now come along, sis. Time to go see the doctor.
Jasmine: (addressing a camel while staring vacantly into space) Why hello, doctor. How are you?
But the funniest moment in the movie has to be Abu bitching Aladdin out in monkey speak, ending with his sarcastic monkey-speech impression of Jasmine.
No, the funniest part is the look on Abu's face when Aladdin manages to spin the monkey-tantrum into fuel for seducing Jasmine. His expression is one of rage, disbelief, and confusion all rolled into one face.
And then Abu sets to freeing Aladdin...with a set of lockpicks. How often does Abu have to bust Aladdin out of handcuffs?
"I think it's time to say goodbye to Prince Abooboo."
After Aladdin exposes Jafar:
Iago: We gotta get outta here! We gotta get out! I gotta start packing, your highness! Only essentials, we gotta travel light. I'll bring the guns, the weapons, the knives... And how about this picture? I don't know, I think I'm making a weird face in it?
He then makes said weird face, complete with buck-teeth.
At the very beginning, there's a scene where Aladdin meets a noble, heading to the Palace on his horse. As the rude man rides away, Aladdin hollers out:
Aladdin: "Look at that, Abu! It's not every day you see a horse with two rear ends!"
Not only is the horse also offended, but he realizes it's an insult before the noble does.
"Al, what are you doing? Why are you bringing me into this?"
"Tell her the TRUTH!"
Jafar trying to hypnotize the sultan the second time.
Sultan: I... will order... the princess to... (snaps out of it) But you're so old!
It becomes about ten times funnier when you hear the censored version of this scene (basically replace the word "marry" with the censor bleep used in TV shows and it becomes even funnier)
When Iago's impersonating both Jasmine and a flamingo, another actual flamingo gets the goo-goo eyes for him, tongue hanging out and everything. After tricking Aladdin, he turns around mid-evil laugh to come face to face with aforementioned lovesmitten flamingo...
Iago: Ya got a problem, Pinky?! (kicks the flamingo over) Jerk.
The Ironic Echo when Jafar gets everything that's coming to him:
Aladdin: eeeeety-bitty living space.
"But remember: Beeee yourself!"
When Snake!Jafar has Aladdin in his coils, Iago tries to goad Jafar into crushing him and Genie comes along and nonchalantly whacks him.
"Squeeze him Jafar! Squeeze him like a... AWK!"
"Jafar! Get a grip!" [GLOMP] "Ack! Good grip..."
Jafar was described as "Seņor Psychopath" by the Genie, who also briefly changes his face to Jafar's.
To anyone with a hint of genre savviness, the Sultan innocently addressing the scary man in the Obviously Evil costume as "my most trusted advisor".
All of Jafar's puns during his final battle with Aladdin.
Jafar: (to Jasmine, who's in an hourglass) Your TIME IS UP! (to Abu, who's been turned into a toy monkey) Don't TOY with me, boy! (to Carpet, who's been unraveled) Things are UNRAVELING fast now! (to Aladdin, when he's surrounded by swords) Get the POINT? (again to Aladdin, when he breathes fire) I'm just getting WARMED UP!
The look on Iago's face when he spots Aladdin trying to sneak up to the lamp.
When Jasmine kisses Jafar, both Abu and Iago adopt identical expressions of shock and disgust. Aladdin is also squicked out.
Iago's rant after the Cave of Wonders eats Gazeem cracks me up every time
Iago: I can't believe it! I JUST DON'T BELIEVE IT!! We're NEVER gonna get a hold of that stupid lamp! Just forget it! Look at this! Look at this! I'm so ticked off that I'm molting!
Iago:: OK... OK, you marry the Princess, all right?! And then, then you become the Sultan!
Jafar: *smiles evilly* Marry the shrew. I become the Sultan. The idea has merits.
Iago:: *Excitedly* Yes, yes! Merits, yes! And then we drop *makes himself look plump like the Sultan* "Papa-in-law" and *makes his shape petite* the little woman off a cliff *Divebombs off Jafar's staff* EYAAAAAAHHH! KER-SPLAT!! *laughs*
Jafar: I love the way your foul little mind works!
Genie: Quick! Quick, wish for something outrageous, say "I want the Nile." Wish for the Nile, try that.
Aladdin: Uh, I wish for the Nile!
Genie: NO WAY!! *laughs* Oh does that feel good!
Possible bad Stealth Pun there; Aladdin got "denial," just like he wished!
While fleeing the Cave of Wonders:
Aladdin: Abu! Abu, this is no time to panic! [sees they're flying straight into a wall] Start panicking!
"They're after me! They're after YOU?"
Iago's Establishing Character Moment. Having spent his first few minutes on screen acting like a normal parrot, he breaks character when Gazeem goes to enter the Cave of Wonders;
Iago:Awk! The lamp! Awk! The lamp! [quietly, to Jafar] Geez! Where'd you dig this bozo up?
In fact, anytime Iago suffers. Like when he's powering Jafar's clockwork contained-storm generator and gets pulled into the gears. When he finally is shot out he's without his feathers.
Iago: With all due respect, your rottonness, couldn't we wait for a real storm?
During Aladdin's fight with Snake!Jafar, Genie becomes a cheer squad and cheers for Aladdin. Jafar tells him to shut up and Genie responds with this gem;
Genie: *complete deadpan* Jafar, Jafar, he's our man. If he can't do it, GREAT!
"Hello, Aladdin. Nice to have you on the show. Can we call you Al? Or maybe just Din?"
"Prince Ali" is outside the balcony on Carpet, desperately trying to describe how he can't possibly be the guy she met in the marketplace because he has "servants who go to the marketplace for my servants." Jasmine and Rajah turn to each other to share a look of pure "is this guy for real?" The way Jasmine purses her lips just seals the deal.Just look at it!◊
When Jafar thinks he has the lamp after leaving Aladdin and Abu trapped in the Cave Of Wonders.
Aladdin tricking Genie into getting them out of the cave without wasting his first wish. Especially funny is when Aladdin dismisses him and tells Abu that they'll have to find a way out themselves.
Genie: Excuse me? Are you lookin' at me? Did you rub my lamp? Did you wake me up? Did you bring me here? And all of a sudden, you're walkin' out on me?! I don't think so! NOT RIGHT NOW! YOU'RE GETTIN' YOUR WISHES, SOSIDDOWN!!!!!
The scene when Aladdin takes on Abis Mal's gang in the beginning is both this and a Moment Of Awesome. Near the end where Aladdin is flying out on the carpet, Abis grabs on and gets taken for a ride. Abu steals the jeweled flower from Abis, who cries "That's mine!" and moves to grab Abu- letting go of the carpet. As gravity takes hold, Abu watches with a smug look on his face.
Genie and Carpet playing pool. Genie is espousing how pool is a "man's game" and implying that, as a living rug, Carpet is at a severe disadvantage. Carpet wins. On the break.:
Genie: Meh. Pool's a dumb game anyways.
"But you'd be surprised what you can live through."
Note that this was only funny when Genie said it as it came directly after some Amusing Injuries. The implications are made terrifying when Jafar says them and later it becomes heartwarming when said by Iago.
The King of Thieves
Right from the beginning, Genie sets the tone:
Genie:(looks at the flickering, lackluster "Aladdin" sign he conjured) Awww... Some of you don't believe!
Genie's red carpet report for Aladdin and Jasmine's wedding in "King of Thieves", especially the ending.
Genie: "Once again, this broadcast is brought to you by "Sand". It's everywhere! Get used to it!"
Code Red! All manner of troops converge on Aladdin's father (it's a long story), ending with about a hundred Genie-cops pointing guns at him: "Do not attempt to move, or we will be shooting ourselves."
Aladdin rubbing his temple in that "I am not being paid nearly enough for this" way.
At the end of this scene, Genie confronts Cassim:
Genie: (toughly) So you're Al's dad...and you're the King of Thieves... Well, I got just one question for you, pal.
Genie:(becomes a waiter and asks politely) Will you be having the chicken or the sea bass?
Genie spontaneously transforming into Pumbaa and saying "Hakuna Matata!", then transforming back and saying "Whoa! I was having an out-of-movie experience", as though this particular transformation was against his will.
The return of Iago's conscience. Apparently, Iago chained him up and dropped him into the ocean.
Aladdin: You lost this battle the moment you made Jasmine mad.
Mozenrath: Oh no! I've angered the princess.
Aladdin: You don't get it. I've seen her mad.
Mozenrath: Oh, should I tremble at the painted toes of her dainty little feet?! I don't think so!
For one of Mozenrath's coolest and funniest moments, look here.
A merchant tries to sell Saleen a fish... whom she apparently knew.
Saleen: Charlie? You reckless fool.
At the end of the episode that first introduced Mozenrath, Aladdin and his friends have been manipulated to helping Mozenrath capture a creature, the Thirdac, that eats magic which he plans to use for his own ends. Aladdin is furious and returns to stop Mozenrath. He threatens that he'll release the Thirdac and sic him on Mozenrath if Mozenrath doesn't send it back to where it came from.
The opening of the episode "Sneeze the Day" opens with Aladdin, his friends and the guards chasing a jewel thief in Agrabah. He nearly gets away on on a passing cart, but smacks his head on an arc and falls off. When he gets back up, he sees Genie charging him in football gear. The look on his faceis priceless.
There is also the thief's Shout Outs to the movie.
The Lost City of the Sun is full of it.
Mozenrath towards his mooks for trying to slink away "while I'm ranting!"
"It appears Shamash had quite the sense of humor"
Iago getting the sprites to go on strike
And the Mozenrath notices the disguised-as-sprites Genie, Iago, and Abu look odd for sprites.
Genie-sprite: Uh...we're from Ohio.
From the guest villain Chaos (voiced by Matt Frewer): "But I never liked Fate. Predestination goes against the grain. Besides, he cheats at cards."
The Disneyland stage show
The Disneyland stage show gets one hilarious one close to the end, where Iago (probably as a Shout-Out to Return of Jafar) tries to convince the good guys that he's reformed, honestly, and starts singing about how he's become "A whole new biiiirrrd...!" Needless to say, nobody buys it.
This troper saw a performance several years ago where the Genie said after being freed from the lamp "I'm free! I feel like Martha Stewart!"
What's great about the stage show is that periodically, the Genie's pop culture references change to whatever's most popular during that time. As this troper recalls, the Genie once introduced himself as Captain Jack Sparrow.
This troper recalls another reference when a certain game show was popular at the time: