BurningLeaf (Red x Leaf): Specifically, their original designs from the first generation, though they are cute together in their remake designs too. I just think these two look cute together. I remember seeing a comic for some sort of craft book where these two were interacting, and they seemed cute together. Red was more hotheaded and risky, and Leaf was more sensible, but sweet.
Conflict (Blue [Green] x Leaf): In this case, I mean the remakes in particular. I like how Blue has a little more interaction with the player in the remakes, and he seems like a cool guy in HG/SS especially. I kind of view his teasing here more as good-natured ribbing than outright bullying like in the original, and I played as Leaf, so it just sort of clicked.
Hanada (Red x Misty [Kasumi]): Especially FR/LG Red. This one was mainly fan art that got me into it. I can't really explain right now, but something about it just seems to work, especially if we're talking stoic!Red as opposed to hotheaded!Red. Something about a mature, quiet guy and a tsundere girl seems cute.
LittleBrotherNoLikeShipping (Brock [Takeshi] x Daisy[Nanami]): Assuming Brock in-game has a similar personality to in the anime, they just seem like a good match. Daisy is kind, caring, and mature- just the kind of girl I can see Brock with.
Expert (Professor Oak [Dr. Okido] x Agatha [Kikudo]): She seems to know a little bit about him, and they just seem like they'd be interesting together since they're two fairly powerful trainers. She says he used to be handsome- I could see him battling her to prove he hasn't lost his touch.
(Lt. Surge [Matis] x B/W Mom): I read a theory on TV Tropes about the possibility of Lt. Surge being Hilbert/Hilda's father, and it just seems to work. I could see him rubbing off a bit on Hilbert/Hilda, and it'd explain why he's not there in B/W- he's at work (although, Hilbert/Hilda's dad could just be dead/divorced, too- but theories are more fun!).
Psychic (Will [Itsuki] x Sabrina[Natsume]): It's hard to explain, but I just think they'd be interesting, especially since Sabrina is a little more confident-seeming in the Johto games. Also, they're both psychics.
Control (Bruno [Siba] x Lorelei [Kanna]): I have this weird habit of pairing up the first two members of the Elite Four when I'm not pairing them with anyone else. They both seem fairly cool and collected, I guess.
WikiError (Lance [Wataru] x Cynthia [Shirona]): They just remind me of each other so much. Both help (somehwat) with taking down the villainous team, both sort of have that same "epic" feel to them, and both appear in Generation IV (in the same game if you have Arceus). Both of them just give off such a similar vibe it's hard to ignore.
(Bill [Masaki] x Brigette [Azusa]): They seem like they'd be a cute, mature couple. I could see them working on PC problems together a becoming some sort of technologically-savvy duo.
Via (Celio [Nishiki] x Lanette [Mayumi]): Between Lanette's pack rat tendencies and Celio just giving off a "dork" vibe for reasons I can't explain, they just have so much potential for adorable awkwardness. They both look up to Bill too, I assume, since Lanette was a co-founder of the PC.