In the interquel comic series of Avatar: The Last Airbender called The Promise, Katara shows a mild case of this. She feels a bit upset that Aang hangs out with the Air Nomad fan club more than her, making her feel left out. But this is resolved (somewhat) when Aang explains that the fan club reminds him of his old home. That, and he loves her.
She's shown a bigger case of this in The Waterbending Scroll, though. This is due to not getting Waterbending right instantly while Aang, being an Airbending Avatar, did. This causes her to yell at him about it only to feel guilty and apologize, and she also put the others in danger due to stealing a pirate's scroll. She gets over all this, though.
In Barbie in a Mermaid Tale, despite being of royal blood, Eris can't spin Merillia. This makes her very jealous of her sister Calissa.
Beetlejuice has a tendency to be a bit of a Crazy Jealous Guy whenever anyone tries to monopolize Lydia's attention, but he goes full-on this trope in one episode. Prince Vince becomes so enamored of Lydia that he actually proposes to her, causing Beetlejuice to almost literally explode; he has steam coming out of his ears and his eyes are flashing multiple colors.
Ben 10 has multiple exemples of this. Considering the protagonists gains Famed In-Story starting with the third installment of the show, that's kinda understandable:
Captain Nemesis, despite being himself a famous superhero as well as possessing his own company, developped a jealousy when Ben starts becoming more popular than him (ironically, Ben himself admired him then). He first attempted to get back credit in a so-called friendly competition with him, but ends up humiliated (the only round he is able to win is only thanks to part him cheating and part Ben's Omnitrix malfunctionning). Unable to stand this, he turns evil as a result. By his second appearance, he has gone as far as becoming a murderer.
A more light-hearted exemple than the two previous ones, minor villain Billy Billion from Omniverse has his whole motivation running around the fact he was jealous of Ben for getting more attention at school than him.
Code Lyoko has Sissi Delmas who loves Ulrich and is jealous of the relationship between Yumi and Ulrich — so she tries to make Yumi jealous in turn (sometimes successfully). Also, when William Dunbar enters the scene in Season 2, Ulrich shows serious envy of William's easy flirting with Yumi, while he himself Cannot Spit It Out.
"What You Want" shows Tucker being envious of Danny's ghost powers. It's a kick in the teeth to him especially because Danny was once on equal terms with him before he got his powers, making him (from Tucker's perspective) "superior."
In "Cassie the Green-Eyed Dragon" on Dragon Tales, Cassie takes her cute little baby brother Finn to school and gets jealous when everyone pays him attention and doesn't notice her achievements. As this is one of those shows that teaches kids how to handle their emotions, Quetzal, the teacher, helps her by explaining how we all feel jealous sometimes and gives her some help to feel better.
An episode of Disney's Hercules (called, appropiately enough, "Hercules and the Green-Eyed Monster") has Icarus being jealous that his drama teacher is marrying his father, and thus getting most of his attention, and disrupting the wedding with Pandora's box. He is then consumed by Jealousy, as in swallowed whole by an Anthropomorphic Personification who has been feeding on his envy.
Jem is loaded with this. The Misfits want to destroy the Holograms because they're jealous of their success, Eric Raymond wants to destroy Jerrica Benton because he's jealous of her ability to run a music company better than him, and Jerrica is actually jealous of her own alter ego because of of the attention Jem receives that Jerrica can't get for her own accomplishments.
Heloise on Jimmy Two-Shoes gets extremly hostile over Beezy's friendship with Jimmy, which often results in episodes of her doing terrible things. For that matter, any supposed instance of Jimmy showing attention to anyone but her can lead to trouble. There was even a role reversal in one episode where Heloise managed to make Jimmy jealous, despite being Oblivious to Love.
Alexandra's reason for wanting to be the lead singer of Josie And The Pussy Cats is jealousy of Josie, both because of her musical success and the fact that Alan has eyes only for her.
Mr. Cat is extremely jealous of Quack Quack, because the latter is far more talented than he is, which results in him always being in second place.
Pretty, the show's Alpha Bitch, gets jealous of Kaeloo whenever she gets something cool that Pretty doesn't have. Bonus points for the fact that Pretty acrually has green eyes.
The two main characters in Kim Possible encounter this in the third season and The Movie, due to a Romantic False Lead and a new friend with a kickass wheelchair and video games. There was also Kim "jelling" over how close Yori seemed to Ron. It's kind of a coincidence considering Kim really does have green eyes.
Kim gets jealous over Ron at almost the drop of a hat: she also gets jealous when he becomes good friends with Felix in "Steal Wheels," and gets very angry over the time he and Bonnie spend together in "Homecoming Upset" - a lot more justified that time, however, as they were dating at that point and Bonnie was doing everything in her power to rub it in. To her credit, she manages to direct almost all her anger at Bonnie and not Ron.
The first season of The Legend of Korra features a Love Dodecahedron. So naturally, this trope comes out in full force. Korra is initially standoffish towards Asami, who was dating her own crush, Mako. When Korra decides to date Bolin, Mako gets jealous in turn due to his own unrealized feelings for her. As Mako and Korra start to get closer and act more affectionate to one another, Asami displays green-eyed tendencies toward them herself, though it's played with in her case as she's shown to be more angry at Mako for his cheating and unwillingness to be honest with her about it. When the dust finally settles at the end of the season, Mako breaks up with Asami amicably and hooks up with Korra.
In the second season, it becomes clear that the Arc Villain, Unalaq, Korra's uncle, and chief of the Northern Water Tribe, is deeply jealous of his older brother Tonraq, Korra's father. He was so envious of his brother's position that he engineered his banishment so he could become chief. Korra also suggests that Unalaq's desire to train her stems from his envy of the fact that Tonraq sired the Avatar.
In Miraculous Ladybug, the protagonists are quite possessive of each other despite not actually being in a relationship. The "Volpina" episode has an Aesop about it when Ladybug's excessive cruelty towards one of her "rivals" renders the girl vulnerable to Hawkmoth's brainwashing.
Princess Luna transformed into Nightmare Moon because she was jealous of all the attention her sister Celestia received. After being banished for a thousand years, she is finally cleansed of her evil and jealousy by the Elements of Harmony and makes amends with her sister.
Trixie is implied to be this towards Twilight Sparkle. Confirmed in "No Second Prances" when she admits it to Starlight Glimmer.
Rarity also suffers from this when Fluttershy becomes a famous model in the episode fittingly titled "Green Isn't Your Color." In an interesting handling of this trope, Rarity is actually very disappointed in herself for being jealous of her friend's success.
Spike gets this towards Owlowiscious in "Owl's Well That Ends Well," thinking Twilight has replaced him as her assistant. It turns out she only got Owlowiscious so Spike could finally have a break from all his hard work.
Everyone thinks Twilight is this in the second season finale, "A Canterlot Wedding," when she begins accusing her brother's fiancee of being evil due to her Bridezilla behavior. It turns out Twilight is Right for the Wrong Reasons.
Sweetie Belle gets a bad case of this in "For Whom the Sweetie Belle Tolls." Her resentment over Rarity "stealing" the spotlight is serious enough that Princess Luna feels compelled to help her get over it. Luna even mentions that she's been where Sweetie Belle is.
Discord becomes one in "Make New Friends but Keep Discord" after learning that Fluttershy has invited a new friend to the Grand Galloping Gala instead of him. His eyes even erupt into green flames when he spots Fluttershy's hoof on said new friend's shoulder, becoming a quite literal example of this trope.
Inplied to be one of Starlight Glimmer's motivations in the 2-parter episode "The Cutie Map." Later confirmed in the "The Cutie Remark", but what Starlight is jealous of isn't the Mane 6, but real friendships based on differences like theirs remaining strong, while her own friendship fell apart because of a difference.
Twilight suffers this in "What About Discord" when Discord pranks Twilight into thinking that the rest of the Mane Six had fun with him while she was away. Spike tries to tell her it's okay to not be involved in anything and Twilight tries to say that, as the Princess of Friendship, she should be above such notions, but she isn't.
Often a major reason for Bluto going after Popeye the sailor usually does a better job fixing/building something than his big rival. Occasionally inverted, but a dose of spinach always lets Popeye win the final round.
Princess of The Powerpuff Girls became a supervillain because she was envious of the Powerpuff Girls ("If I can't be a Powerpuff Girl, then there won't be any Powerpuff Girls!"). In "Superfriends", she becomes jealous of Robyn, who has become the Girls' best friend, the only thing theSpoiled Brat has ever wanted but could never have. ("Why would the Powerpuff Girls want to hang out with you when they could be friends with me?!!...")
In Puff the Magic Dragon, Puff tells Jackie that the mean-looking clouds overhead are jealous of the stars, because the stars can fly so much higher than they can. As fate would have it, a falling star lands in their boat, and the clouds all have an Evil Laugh; Puff looks at them in disgust, saying, "They're so happy when a star dies." (She's not dead yet, though, and they can still save her.)
The infamous Frank Grimes comes across as this. Homer did get him in trouble with Burns, but Grimes' quest to destroy Homer's life came after Homer tried to make it up to him by inviting him to his house for dinner. Seeing his big house and family only made Grimes even more bitter.
Subverted with Cecil Terwilliger. It seemed like he wanted to kill his brother for having been chosen as Krusty's sidekick but he just really wanted the money.
In "Date With Destiny'', Starfire becomes something of a Yandere once she finds out that Robin is taking a bratty Daddy's Girl to her prom (as part of the Big Bad's blackmail).
Robin also becomes rather green-eyed over Starfire when she's getting married in "Betrothed." Cyborg explicitly teases the boy about it, saying, "You sure you're not just, y'know... jealous?"
Tygra from Thundercats 2011 seems to have been suffering this for a long time, in regards to his little brother Lion-O. This is both for Lion-o being heir despite Tygra being seen as the better one and for him supposedly having the affections of Cheetara. Later, it's revealed that Cheetara always liked Tygra and Lion-O is happy for them (though he chastised Cheetara for her Hands-On Approach in advising and helping him).
An episode of Tiny Toon Adventures had this as its Aesop, but the characters don't realize that the warning about a Green-Eyed Monster isn't talking about a literal monster until the very end.
Thrust, one of Starscream's clones in Transformers Animated, embodies his creator's envy. This is appropriate, as he's the only clone who doesn't appear in the cartoon or the toyline - he only showed up for the second Allspark Almanac.
Yogi's Gang: The Envy Brothers. They want to take over the circus where they work because they're envious of their boss for owning it and try to accomplish it by using a ring to make everyone envious. Bonus points for wearing green and making their victims' eyeballs green. When that fails, they try to go to outer space because they're envious of astronauts for doing so.