Craig Tucker and his friends are this to the main four boys in South Park
Mandark is Dexter's rival in Dexter's Laboratory. The two clash a lot though Mandark does have a serious thing for Dexter's sister Dee Dee.
Plus, the episode "Dee Dee's Rival" did a Gender Flip of this trope by pitting Dee Dee against Mandark's sister, who was apparently created specifically for the episode and proceeded to never be mentioned again. She nonetheless went through the complete arc of this trope during her brief screen time, right down to the grudging respect (by the end of the episode, she and Dee Dee have decided to be friends).
In Chowder, Endive has been Mung Daal's rival in the catering business for years. Panini should be Chowder's rival, but she chooses to be his YandereStalker with a Crush instead, so Chowder's actual rival is Gorgonzola.
Apparently Panini was originally supposed to be just that when the creator pitched the series. He decided to retool her when it got picked up.
On American Dad!, Roger invokes this trope in a horse race when he tells one of the other jockeys he got it on with his wife. Roger did this deliberately because he thought the race would be more interested if he had a rival to compete against.
When Steve put together peewee football team to compete against his father's one of his recruits is a Chinese kid named Li-Fung who doesn't speak English. Steve's Japanese friend Toshi attacks for stealing his bit.
In one episode of The Simpsons "Lemon of Troy", Bart has Shelby (a doppelganger from a rival town, Shelbyville) as a rival. In fact, Milhouse also has a rivalry with his own counterpart (also named Milhouse) from the same town.
In "Lisa's Rival", Lisa forms a one-sided rivalry with the new girl, Allison Taylor. Too bad she is Demoted to Extra for the remainder of the series, even after their reconciliation. (It seems any new girl in school is destined to be Lisa's enemy - see also "Lard Of The Dance" and "Bye Bye Nerdie.")
In can also be said that Marge has an occasional rivalry with her gossiping fair-weathered acquaintance, Helen Lovejoy.
Mr. Burns also has his own business rival at the Shelbyville Nuclear Power Plant, Aristotle Amadopolis.
Then there's Seymour Skinner's rivalry with Principal Valiant of Shelbyville Elementary School, due to the school's better funding and academics.
Lisa claims that Maggie's arch-rival is Gerald, the baby with one eyebrow, though we never see them do anything other than glare at each other while ominous music plays.
And then there's Homer's iconic and extremely one-sided rivalry with his neighbor Ned Flanders. Homer despises him for being successful in all the ways that he isn't, but Ned views him as a close friend.
Trixie is often portrayed as Twilight Sparkle's rival in fan works, and the episode "Magic Duel" canonizes it. (Twilight tends to think differently.)
Rainbow Dash finds a rival in Lightning Dust "Wonderbolts Academy". Unlike Trixie, Lightning is clearly able to match Rainbow in ability, the first rival to actually achieve this with a mane character.
The Flim-Flam Bros. establish themselves as rival apple cider sellers to the Apple Family in "The Super Speedy Cider Squeezy 6000".
Pinkie Pie finds a rival party thrower in Cheese Sandwich in "Pinkie Pride", who, as it turns out, is even better at party planning than Pinkie is. Unlike previous rivalries, he is firmly a Friendly Rival by the end.
In "Rarity Takes Manehattan", Suri Polomare becomes Rarity's rival as a fashionista, and like Trixie, does not match up to Rarity in ability and relies on being an Opportunistic Bitch to get ahead.