Starting with main characters, when I was younger, I shipped Ash with Misty, but later I realized, he doesn´t deserve her and is too oblivious, so his only love will be Pikachu. Forever. Okay, I confess I ship him also with Tabithas Mightyena.
But Pikachu loves his ketchup. It will be interesting love triangle.
(I realized, I don´t ship Misty nor Brock with anyone anymore. Strange.)
May + Drew. It was obvious for me. But she also had some funny interracions with James, so wynaut ship her with him, too?
But game!May goes defininitelly with Steven. I don´t consider player characters to be ten or just a bit older, so no predophilia here.
Speaking of Steven, here goes my first bicycle. There is game!May. There is Cynthia. Jasmine. Gardenia. Shelly. (Shauntal and Caitlin).
After seeing Junior cup opening episode, I ship Caitlin + Cynthia as one-sided one from Caitlin.
And Cynthia is another shipping bicycle. Not counting the above mentioned, there is Paul, ice-cream, Lance, Ghetsis (really! I have amazing headcanon about this), Riley (but he is Steven in disguise in my headcanon, so it doesn´t really count), Cilan and I´m sure I´ve still forgotten someone.
Speaking of champions, Lance slept with every girl/woman about his age in Pokéworld (And Burgh). He and Clair is the only incest shipping I support. And maybe the ship with Iris is mentionable. (Also I hope he´ll meet Georgia in the series. It´ll be hilarious).
And I ship his Dragonite with Cynthias Garchomp.
Back to the main cast, there is Dawn + Conway and maybe Gary (who has no other ship on my list and I don´t know why because I don´t dislike him).
Yes, I ship Cilan with Cynthia, Iris, Burgundy and Layla.
For Iris they´re surprisingly no other ships than above mentioned.
Now there are vilains coming.
Giovanni is shippable with everyone, but that one-sided with Meowth is nice. Otherwise Ariana is probably the best choice.
I will be a bit boring now boring, but I ship Jessie with James. (And maybe Harley, for the fun).
Otherwise will be James tortured by Jessiebelle. (But I ship her with Gardenia, too). And I ship him with Delia. Really.
Shelly and Tabitha is obvious choice, even though I hate all the mushy fanfictions about them. They hate each other, but it often ends… ehm… go figure. She is shipped with Cynthia in purely friendly way. I ship her with Steven (because I like to think she was one of the spies in Devon and she wrote the weird description of Steven in the Pokénav in Emerald). I ship her with Brawly. (And of course Lance, as he is shipped with every woman character).
While I can understand shipping Jupiter with Looker, I prefer shipping her with Cynthias Garchomp. Just because I can.
There are some other ships, such as Clair + Drake (Hoenn).
Cheren with Bianca or with Jasmine. (Don´t know why, it just happened).
Jasmine with Roark.
Shauntal + Lucian.
And all the lol ships such as Ghetsis & Remoraid.