Envy of the Seven Deadly Sins in the DCU can turn anyone, hero or not, into a Green-Eyed Monster. Under its influence, Green Arrow once succumbed to his own envy of Batman over, well, everything, and tried to kill him.
Why does Lex Luthor hate Superman? Because Superman is more powerful than Lex, and he won the hearts of Metropolis without any effort at all. Confirmed in Blackest Night, wherein Lex is bound by Wonder Woman's Lasso of Truth and is forced to admit to himself and everyone around him that: "The truth is... I really want to be Superman." It also probably isn't a coincidence that modern portrayals of Lex in the comics often have green eyes.
In Krypton No More, co-worker Terri Cross flirts with Clark Kent. And Lois Lane is not happy about it. She isn't happy at all. She is actually fuming.
Supergirl's first Arch-Enemy was Lesla-Lar, an accomplished Kandorian scientist who began antagonizing Kara because she was jealous of the praise that people of Earth gave Supergirl.
Lesla-Lar: I envy and hate her! The honors that I, Lesla-Lar, have earned in Kandor as a scientific genius are as nothing compared to the acclaim the people of Earth will give Supergirl when they learn of her existence!
In Demon Spawn, 'Nasty' Luthor glares and fumes when Linda and Geoff kiss.
In Supergirl Vol 1 #7, Supergirl and Zatanna spend a while seeking out a man called Tony -whom they have a crush on- and struggling to save him. As soon as both women learn that he has a fiancée, they refuse to speak to him.
In Supergirl Vol 2 #20, Linda's friend Joan is jealous of Linda when she finds out that her friend is meeting Clark Kent, nationally famous newscaster. Her jealousy goes away when Linda explains Clark is her cousin.
Linda: Well, we could try to make some friends. I mean, we always sit as far away from everyone as possible. Which, you know... kinda means we're the ones banishing ourselves... Lena: What?! I thought I was your friend! Linda: Uh... You are. I just meant— Lena: Then what do you need them for? Linda: I just thought that maybe... Lena: My friendship isn't enough? Is that it?
Green Lantern: Guy Gardner hates Superman because his girlfriend Ice admitted that she thought Superman was cute. He still hates him to this day.
Batman: Thomas Elliot, a.k.a. Hush, dedicated himself to destroying Bruce Wayne out of sheer envy. The way he sees it, Bruce was "lucky" that his parents died when he was a kid (and getting all of their money) — Thomas, on the other hand, had to go to all of the trouble of cutting his parents' car's brakelines and later smothering his horrible mother to get access to their money. Thomas, of course, being an amoral sociopath, doesn't grasp that Bruce's parents might be different from his parents, making this a rare case of someone consumed by insane jealousy not because of what someone else has done or accomplished, but literally for NO REASON AT ALL.
Mona Menise is already a menace, but when she realizes her crush Steve Trevor is in love with Wonder Woman she gets much much worse and decides to murder them both.
Wonder Woman (1987): Veronica Cale is dangerously jealous of Wonder Woman. She thinks that an Omnidisciplinary Scientist billionaire magnate who worked her way up from rather humble origins like herself is more deserving of the title than a magical princess like Diana. If she wasn't also a Mad Scientist who kills innocent people and turns others into living weapons she might actually have a point.
Robin's Young Justice teammate Secret tracks down his girlfriend Spoiler and attacks her in her own home after learning that her crush is dating someone other than herself, and generally fights with Spoiler every time she sees her due to her jealousy.
The Mighty Thor: Loki is Marvel's personification of this trope to the point that he has actual green eyes. His constant envy of his elder brother, Thor and his need for love from his father warp him into a villain. Most of his mischief is about getting attention and love. His history as an abused child doesn't help. Neither did Odin's blatant favoritism towards Thor. Odin adopted Loki out of obligation and guilt. Ironically he creates his own destruction by doing so.
In the Fantastic Four, this is the reason Doctor Doom hates Mr. Fantastic. He can't stand the fact that Reed Richards is smarter than him, and has beaten Doom every time he has tried to kill Reed and/or Take Over the World. In addition to those few extra IQ points, Reed also has everything else Doom doesn't have, from worldwide respect all the way down to unmarred good looks.
Spider-Man: J. Jonah Jameson has both Envy as his motivation and Greed as the vice that leads to the motivation for constantly making Spider-Man's life hell. He's privately admitted that he's jealous of Spider-Man for being so selfless and altruistic for everything he does while Jameson is only concerned with what he can get out of everything he does, so he tries to find or manufacture something, anything to make Spider-Man look worse to make himself feel better. That, and constantly attacking Spider-Man in his newspaper sells massive amounts of papers.
It should be noted, however, that this characterization was from The Amazing Spider-Man #10 back in 1964, and has mostly been ignored since then. Most writers depict Jameson as an honest man with a legitimate distrust of people who wear masks, as that can only mean they have something to hide.
Rhona Burchill/The Mad Thinker from Ultimate Fantastic Four is motivated by her jealousy toward Reed Richards, because he got into the Baxter Building Program for Gifted Children instead of her.
Haazen from Knights of the Old Republic (the comics) is this trope — he was consumed years ago by his jealousy of his friend (and later employer) Barrison Draay's wealth, good looks, talent with the Force, and luck in love with the girl Haazen was also sweet on. This lead him to ultimately arrange Barrison's assassination and then spend decades concocting an Evil Plan that would pervert everything Barrison stood for as well as his family name, while ending with Haazen ruling the galaxy from behind the scenes. And if would have worked if Zayne Carrick hadn't convinced Barrison's son Lucien that this wasn't what his father would have wanted.
In the short story in My Little Pony Micro Series Issue #3 Spike, noticing Hayseed's enamor for Rarity, claims she has a fiance and breaks Hayseed's heart.
Apple Bloom in the "2014 Holiday Equestria Girls Special" essentially destroys what goodwill Sunset Shimmer had built up out of pure jealousy because Applejack was spending more time with Sunset than her. Even worse is that Scootaloo and Sweetie Belle get involved in this, too.
Wiske in Suske en Wiske at any pretty girl that is interested in Suske.