Ash and Gary, anyone? Probably one of the first big Foe Yay ships. Many shippers believe that their rivalry started as a way to cover up their real feelings which they were scared by in early puberty. Hmm. Either way, Gary leaves rude messages for Ash where Ash will find them, and Ash has at least once stayed up all night thinking about Gary. Neither of them have had any crushes on girls in the show (except for Ash that one time..), (and Ash would have plenty to choose from if he was interested in girls). Also note the high amount of instances where Ash and Gary hold hands and put their arms around each other...and even an instance where Ash rushes to Gary when he's hurt and holds him in his arms.
And now we have Ash and Trip, who is a major Kuudere, which actually causes the "only a jerk to Ash because he wants him" to hold more water than it did with Paul. To feed the Shippers even more, Trip is one of the few rivals that doesn't piss him off as much as Gary (because Ash and Gary started out as best friends, so the rivalry was more hurtful to him, and Ash and Gary eventually became good friends again) or Paul (because of serious reasons mention above). Even if Trip acts like a jerk, Ash is willing to ignore almost all of his insults. Trip is the only rival where Ash actually dismisses Trip's victory over him particularly the first battle where he declares that it doesn't count, making the shipping issue even worse.
And in BW054 Trip is shown to have a similar personality to Ash when it concerns certain topics and naturally is thrown to Ash's immature levels when they both are fighting for Alder's attention. Of course Ash starts the confrontation by elbowing him out of the way and what's Trip's response? He elbows back.
Also, despite the fact the two are rivals, Ash seems to be looking out for Trip and always tries to impress him whenever he battles before him as shown in BW041 and BW054. Naturally, it usually takes near the end of the battle for Trip to look at the battle instead of looking everywhere else.
Before you fangirls pounce on that, it could also be seen as a senior-to-rookie friendship, as it is natural for kids in Japan to highly respect people more experienced than them, and for the senior to look out for the rookie who respects him back.
Dawn and Zoey. Zoey is a little too touchy-feely around Dawn, her main contest rival. They do act more like best friends, though, so there isn't much "Foe" in this "Yay".
In more Contest rivalry, May and Harley have a bit of this, albeit very one sided on Harley's account. He basically stalks her, tries to trip her up, is willing to manipulate the people around her to get her to lose...but he still follows her around anyway, and seems to have no problem initially being flirtatious with her, despite being very, very, veryCamp Gay.
Excuse me, when was Harley flirtatious with May? ...ignoring the advice parts... If anything, Harley has Foe Yay with Drew or Max (please no pedo...), or anyone else, really.
Yeah, I would have to say Harley was never flirtatious with May. If anything, he was disgusted with her. Nevertheless, Cookieshipping, as the pair is called, appears to be the top, most popular Harley ship, filled with ship happy fans that try making Harley good (and younger apparently), and thus stripping away his character until he is an empty shell. Alternatively, especially in fan fictions written by those that don't ship it, Harley is a creep who literally stalks May in a pedo way, and it's up to Drew or whoever the hero of choice is to save May.
Cilan and Burgundy. Burgundy is incredibly obsessive over Cilan for beating her in a Gym battle. In her later appearances, she's rather kind and civil to everyone (people and Pokémon alike) except him. She's clearly a tsundere.
It gets better: in her recent appearance, she and Cilan actually agreed to do a battle commentary together, opening it up with a Team Rocket Motto-esque sequence.
Let's not forget that when Cilan is dishing out evaluations and Burgundy is nearby, she always is the one giving Cilan's advice and critique the most attention. Point in case: the Club Battle tournament at Nimbasa City.
Also, Iris and her rival Georgia. Their heated rivalry confrontations frequently feature them veryphysicallyclose toone another. There was also that instance where Luke's Zoura transforms into Georgia and Iris proceeds to touch it all over in order to use it like a puppet to mock Georgia.
And in BW 083, when Iris thanks her for lending her Vanilluxe that saved her life, Georgia seems surprised, blushes and then walks off awkwardly.
Meowth and Pikachu get subtext too. Besides the Ho Yay filled episodes where they get stuck working together, there's an Image Song where Meowth sings about Pikachu in a loving way, and his late voice actor Maddie Blaustein once said she used to play him up as a bisexual.
It's taken up a notch in recent Best Wishes episodes. When Meowth is apparently fired from Team Rocket, Pikachu is the only one that doesn't trust Meowth. However, slowly he starts to trust Meowth and the two seem to hit it off. And then Meowth goes and reveals that he was working as a double agent and Pikachu is PISSED. And we mean really pissed to the point of constantly trying to electrocute Meowth even when Team Rocket makes their getaway. Pikachu was really hurt by the betrayal.
Also from Adventures, Blue (Green in the US) and Sabrina get slashed sometimes, mainly due to their famous battle in the first arc in which Blue uses a pokeball boob trick on her, and afterward leaves the battlefield saying "Bye-byeee!" with a heart put next to the text. In the second arc, the two of them get cuffed together and Sabrina refuses to leave Blue to die, even at the risk of her own life. Afterwards, Blue is shown holding Sabrina when she's unconscious. Also, Sabrina gets hooked up with Red sometimes due to an infamous hot springs scene between the two of them in the third arc.
Mind you, Sabrina's not the only evil team executive who has subtext with a Pokedex Holder. Ruby and Team Magma Admin Courtney look like they have a Dating Catwoman relationship despite Ruby's sexual tension with Sapphire, and Mars of Team Galactic really seems to find Dia interesting. And as expected from the games, N gets Foe Yay with both Black and White, as shown when N sometimes gets a little too close for comfort with Black during their battle and his Ferris Wheel Date Moment with White (until it got unexpectedresults).
Other Pokémon manga is full of this, which is no surprise since the source game are Foe Yayrival and villain heavy:
How I Became a Pokémon Card has Kaede and Erika. They're friends though and it only counts due to the former being a Team Rocket grunt.
Pokémon Golden Boys has Black and Gold. Black is just the same as Silver in the games however with extra camp.
In the same vein, Mareanie and its evolution Toxapex are capable of breeding with Corsola, which they mercilessly prey on in the wild. Umm...
N and the BW protagonist became one of the most popular Pokemon ships very quickly. It helps that N is an Anti-Villain though. The ferris wheel moment where he reveals he's affiliated with Team Plasma is iconic and has an odd resemblance to the ferris wheel dates in the game.
The second game only added more fuel to the fire—though that probably doesn't count, seeing as N and the player character are no longer foes at that point.
Silver angrily stripping Lyra/Ethan makes perfect sense in context but it was inevitable fans would take it a different way.
Though not as well-known as other examples, fans have been known to ship Groudon and Kyogre. The pairing experienced a brief spike in popularity after the first season finale of Steven Universe, where the character Garnet was revealed to be a fusion of two gems named Ruby and Sapphire. As seen here and here◊. (WARNING Spoilers)
Similarly, Archie and Maxie, the leaders of Teams Aqua and Magma respectively, whose passionate rivalry has garnered a lot of shippers who immediately lapped the idea up. The remakes of Ruby and Sapphire only served to exacerbate it.