Archie's Weird Mysteries, natch. In one episode, a sea monster tries to woo Archie by taking on the guise of a girl combining Betty and Veronica's best features, prompting Betty and Veronica to form an Enemy Mine as they think they're the only ones who will fight for Archie. In the finale, a time-travelling future version of Archie is about to tell his past self who he finally got together with, only to be zapped away at the last moment.
In The Avengers: Earth's Mightiest Heroes!, both quiet, reliable Jane Foster and sexy, dangerous Enchantress seem to love The Mighty Thor. However, he just doesn't like the Enchantress. Ultimately, Enchantress stops pursuing Thor's affections after becoming enslaved by Surtur the fire demon, and Jane breaks up with Thor after realizing that dating a superhero might endanger her.
Clone High pushes this one to its logical extremes: Abraham Lincoln is madly in love with demanding, selfish, spoiled, slutty, gorgeous, popular Cleopatra (Veronica), while remaining completely clueless to the devotion of his best friend: spunky, intelligent, independent, creative, semi-goth Joan of Arc (Betty). In the end he realizes that he really loves Joan, etc.
To a much lesser extent, Joan could be considered to be the Archie to Abe's Betty and JFK's Veronica.
Applies to Danny Phantom, where Danny is infatuated with Paulina, the shallow, beautiful "Veronica" of the school, ignoring the pretty, intelligent "Betty" at his side, Samantha Manson. The love triangle isn't clear at the beginning of the show, when Samantha and Danny are Just Friends, but eventually their feelings do grow for each other.
Justice League Unlimited would have Hawkgirl and Vixen in these roles... but the challenge here is to determine who's who to John Stewart's Archie. On one hand Mari/Vixen is a world famous fashion model, very beautiful and glamorous while Hawkgirl is a more down-to-earth character and kinda One of the Boys. On the other, Hawkgirl is a redhaired alien woman with wings, which makes her a lot more exotic than the Earth-born Vixen will ever be.
Also they play this trope a step further making them frenemies rather than downright rivals. To the point that Mari is Genre Savvy enough to rescue herself and Hawkgirl from some enemies... via pretending that she wants to Murder the Hypotenuse.
In Kappa Mikey, Mitsuki is the Betty and Lily is the Veronica to Mikey's Archie.
Kick Buttowski Kick has two girls admiring him, Jackie the Loony Fan is the Betty who openly has a crush on Kick, and Kendall who secretly likes Kick is the Veronica.
Coop from Kid VS Kat has Phoebe the Veronica and Fiona as the Betty who both like him.
In King of the Hill, Nancy Hicks-Gribble has been carrying on an affair with Veronica, John Redcorn, while married to her Crazy Survivalist husband Dale (the Betty).
Monster Allergy has Elena the Betty and Lay the Veronica when it comes to Zick. Lay has this with Zick as Betty and Teddy as Veronica.
Parodied not subtly at all in South Park. In the two parter "Do the Handicapped Go To Hell?"/"Probably", Satan has to choose between his two gay lovers, and the Veronica happens to be Saddam Hussein. And the two rivals keep killing each other, but they're in Hell already, so they just keep coming back. Eventually, Satan just says "forget it" and dumps them both, deciding to forgo having relationships at all for a while. Based on advice from God.
The Movie has a gender flip version with Wendy as the Archie, Stan as the Betty and Gregory as the Veronica. It may have been imaginary, though, since Wendy chooses Stan at the end with no hesitation.
The Spectacular Spider-Man has Gwen Stacy as the Betty, similar to some of her comic book presentations, but it is Liz Allen who is given the status of the Veronica whom Peter goes out with first. Mary Jane only fits the Veronica role for a quick bit of Ship Tease—she went on one blind date with Peter, but during the first and second seasons at least she doesn't harbor much serious interest in him other than as a friend. Whether this would have changed if the show had continued is unknown.
Spider-Man: The Animated Series. Rich, popular, snobbish, born with a silver spoon in her mouth, Felicia Hardy as the Veronica and down-to-earth girl next door Mary Jane as the Betty. And then Felicia gets Character Development, a convoluted deal with Morbius... and becomes Black Cat.
Lance and Ilana have a bit of a Ship Tease in Sym-Bionic Titan. Later on, Lance shows some interest in a girl named Kristin, who is the Veronica to Ilana's Betty. In a gender-flipped version, Ilana bonds with a boy named Jason, who is the Betty to Lance's Veronica.
In The Critic episode "Lady Hawke", Jay Sherman (the Archie) got into a triangle with Alice (the Betty) and his best friend Jeremy's twin sister Olivia (the Veronica). He chooses Alice at the end of the episode.
The Legend of Korra puts Mako in the Archie position, choosing between Korra (the Veronica) and Asami (the Betty). Interestingly, a lot of the traits usually associated with each side are swapped around; ie. Asami is the richer, more traditionally beautiful one, while Korra is the naive, Amazonian beauty from the country (well, Southern Water Tribe).
In Season 1, he dates Asami for several episodes, but eventually chooses Korra after her abduction induces a Love Epiphany.
In Season 2, this falls apart; he breaks up with Korra, has a brief fling with Asami, gets back together with Korra after Laser-Guided Amnesia makes her forget they broke up... and finally ends the season single when they break up again, realizing that their relationship simply doesn't work.
Season 4 finally resolves the love triangle when Korra and Asami end up in a relationship with each other. As such, they effectively both end up as Betties to each other.
In The Secret Saturdays, Doc Saturday could to be the Betty and Leonidas Van Rooke the Veronica for Drew Saturday.
This occurs a few times in The Simpsons. In 'The Last Temptation of Homer', Homer almost has an affair with Mindy (Veronica), but chooses Marge (Betty). He also choose Marge over another Veronica, Lurleen Lumpkin, in 'Colonel Homer'. A gender subversion occurs when Marge chooses Homer (Betty) over an affair with Jacques (Veronica) in 'Life on the Fast Lane'.
Several hypothetical/future episodes have Lisa involved with Milhouse (Betty) while attracted to Nelson (Veronica).
A gender-flipped version in ThunderCats (2011): Lion-O (Betty) has a crush on Cheetara (Archie) which makes Tygra (Veronica) jealous. She chooses Tygra. Later on, a non-genderflipped version Lion-O is now the Archie, with Cheetara being the past Betty to his new love interest: Pumyra as Veronica.
In Pahkitew Island, Ella is the Betty and Sky is the Veronica to Dave's Archie. However, he ends up with neither girl.
In X-Men: Evolution, arguably Jean Grey is the Betty and Rogue the Veronica for Scott Summers/Cyclops.
Also, Cyclops could be said to be the Betty and Gambit the Veronica for Rogue in this series.
W.I.T.C.H. pulled this during its second season with Cornelia as the Archie, Caleb as the Betty and Taranee's brother Peter as the Veronica. This was due to the fact that Cornelia and Caleb broke up in the beginning of the season and Corny took the opportunity to try to catch Peter as a rebound. After Caleb is thought to have been killed, Cornelia realizes that she does still love Caleb and, when he comes back, decides to reconcile with him.