Batman Gambit: Sometimes it's this, sometimes it... well, see below.
Bound and Gagged: And submerged underwater to drown, until Genie saves him.
Character Development: By the final film, he's really grown into a man worthy of being Sultan.
This is best seen in King of Thieves. After breaking his father out of prison, Aladdin returns to face any punishment he might receive, because he realized how much his running away would affect Jasmine due to his own father's abandonment of his family. Aladdin has learned that his actions affect other people, a lesson some people would say more rulers need to learn.
Chaste Hero: Although he's engaged to Jasmine and thusly spends a lot of time at the palace he still seems to live in the abandoned building from the first movie.
Does Not Like Shoes: Even after the Prince Ali charade is over, we see him wear shoes to select events such as his wedding and a few times in the TV show. However, he seems to prefer going barefoot 99 percent of the time.
Losing Your Head: In one episode ("Heads, You Lose") along with Caliph Kapok. Thankfully, Al gets better. By the way, we saw him get nearly decapitated before in The Return of Jafar.
Mr. Fanservice: Reportedly, he was redesigned during development because originally he was deemed not attractive enough.
Must Make Amends: After Aladdin left behind the genie lamp, which led to Iago bringing it to Jafar, then Jafar using it to wish himself to be sultan and the world's most powerful sorcerer, Aladdin said:
"I made a mess of everything; somehow I gotta go back and set things right."
No Social Skills: A mild case, again due to his having grown up on the streets, he often doesn't fit in at the palace. Although he does have a sort of common man's wisdom that impresses the Sultan enough to want to make him his royal advisor.
Flanderization: An odd case of this being due to different actors. Williams' Genie is a screwwball, but also has a sensitive and reasonable side, sometimes acting as a sort of father figure to Aladdin (particularly in King of Thieves). When Castellanata plays him, this almost completely vanishes, and his hyperactive goofiness is played up much more.
Forgot About His Powers: Due to how powerful he is, he has a bad case of this in the series.
And whenever he didn't forget, he had an unfortunate tendency of running into villains with Anti-Magic abilities or otherwise have a similar power level.
Our Genies Are Different: For the most part, Genie was consistent with how the 20th century Western world viewed genies, although he had a few new twists. He was one of the first genies to want to be set free, and the first genie that could not kill.
It may not have been Disneyfication so much as the the writers were simply Nerfing a potential deus ex machina outright.
Anti-Villain —> Anti-Hero: Even in the first movie, he's clearly the lesser of evils in comparison to Jafar. Return of Jafarhas him alternate between Face Heel Turns and Heel Face Turns, but eventually settles on a status that is (albeit barely) in the general direction of good, which carries over into the third movie.
Butt Monkey: The movie writers' mantra: "When in doubt, hurt the bird."
Face Palm: Manages to do this without a face or a palm.
Just a Carpet: He doesn't like being treated as just a piece of decoration, but who would?
Leitmotif: Yes, even the Carpet gets one. You can hear a soft variation of it when they first meet Carpet, followed by a bombastic version during the escape from the cave. It returns as Aladdin and Abu escape the ends of the earth later on.
Ax Crazy: He looks calm and cold-blooded at first, but once he obtains the Lamp's power he loses all his coolness, revealing his true psychopathic nature.
Family Unfriendly Death: He convulses in agony while his skeleton appears in flashes of light in a manner not dissimilar to how electrocution is portrayed.
Faux Affably Evil: Begins as composed, polite and stoic, but gradually reveals the true monster behind the act.
Leitmotif: A dramatic, descending piece that sounds a bit like "Arabian Nights."
Loophole Abuse: Genies can't kill anyone, but in Return of Jafar there's nothing stopping him from setting up people to be die indirectly, say, by leaving them dangling from a rock over a pit of lava.
One-Winged Angel: In addition to the Scaled Up mentioned below, he turns into a Genie. While it doesn't work for him at the time and he becomes Sealed Evil in a Can, he proves in the sequel he's far more powerful than before.
Would Hit a Girl: Even though he doesn't get to the point due to deciding that forcing her to become his love slave via Genie would be much better, Jafar was about to seriously backhand Jasmine when she tossed the wine in his face.
Chained Heat: With Aladdin in the TV finale. Even better, it was a magic chain. If the got along, it was long, disagreeing, short, and if they started fighting the shackles fused together.
You Have Failed Me: It's said in one early episode that he beheads those who fail him. Haroud warns him about doing this, but to no avail, as it tends to just be the two of them after that.
Bastard Understudy: The little backstory that is known about him basically boils down to overthrowing Destane and taking his power for himself.
The Chessmaster: While he is fairly good at making plans, Aladdin and his friends are just as good at foiling them. He spends one episode just sitting on his throne, and it still doesn't end in a complete loss for him.
Dangerously Genre Savvy: He knows how to manipulate Aladdin to do his dirty work for him, that a hero makes a better hostage than a princess, and the convenience of Anti-Magic, to name a few.
Evil Genius: Though he mostly relies on his gauntlet, he's no stranger to creating his own magical tools, or to the knowledge of how to acquire more devastating magical weapons.
What Could Have Been: The third movie was originally going to be about him and Aladdin discovering that they are brothers. However, it was decided that references to the TV series were better avoided.
Word of Dante: Everything you think you know about Mozenrath's backstory. See the Trivia tab.
Xanatos Gambit: He sets one up in his debut episode. Either he will gain control over a magic-devouring beast, or Genie will be gone. Either outcome would leave Agrabah powerless against him.
Badbutt: She mostly stays out of any direct confrontation with the heroes, since the things an incarnation of all evil would do to her enemies in a battle probably wouldn't be very kid-friendly.
Noodle Incident / What Happened to the Mouse?: As part of her mysterious past. At the end of "Eye Of The Beholder" Fasir briefly implies that he and her had some kind of romantic relationship, before something twisted her to evil. This is never brought up again.
Psycho Ex-Girlfriend: It's implied in the episode Eye of the Beholder that she and Fasir were once lovers, though it's never elaborated on.
Anti-Villain: He's probably the least evil of the series villains (not the least effective, Abis Mal is that, but the least malicious) since he's only collecting a debt from the Sultan and doesn't hurt any of the characters before they hurt him.
Jasmine: "Arbutus, I'm not a flower you can keep in your garden! I need my family and friends."
Arbutus: "Ah, yes, human needs. Like you need to hack down my gorgeous trees, and chop them into lumber."
Jasmine: "It's not that simple."
Arbutus: "Indeed! You burn them, for warmth. Creating smoke, to block our life-giving sun!"
Jasmine: "We don't do that on purpose!"
Arbutus: "Is it an accident when you rip and pluck my flowers? Condemning them to a slow death in a vase?"
Jasmine: "Slow death?"
Arbutus: "Your kind, you're all the same! You treat my beautiful living creations as things! Why should I treat you any differently?"
Papa Wolf: He loves his plants as much as Aladdin and the sultan loves Jasmine.
Whole Plot Reference: Arguably, his episode is a variation on the original story of Beauty and the Beast; a man is caught stealing flowers from a magical creature and the creature claims his daughter as payment. And even though Jasmine didn't fall in love with Arbutus, she still had pity for him and tried to stop him and Aladdin from fighting.
Noodle Incident / What Happened to the Mouse?: As part of his mysterious past. At the end of "Eye Of The Beholder" Fasir briefly implies that he and Mirage had some kind of romantic relationship, before something twisted her to evil. This is never brought up again.
Mythology Gag: Possibly; in the original Aladdin legend, there were two evil sorcerers, the second being the vengeful brother of the first one. While Jafar was basically a Composite Character of the two of them, Nasira brings back the basic idea.
Scaled Up: Nasira doesn't need to transform into a cobra. She already looks like one.