Well, I tend to approach the stories of Pokemon games (at least, the ones I like the most) in a very fandom-y way, thinking about the details of the characters' personalities and roles and "headcanoning" pretty much everything I can, so theoretically I'm exactly the type who would be a shipper, but the whole concept of romance is basically a big ??? to me so it's not an angle that comes up often. My feelings on most ships basically amount to I see value in that idea but hold little attachment to it. But there are definitely a few random ones that I just happen to like more, for some reason.
One pairing idea that I think is really good but haven't seen anyone else talk about (like, I think I might have actually been the first to come up with it, haha): Hau x Zossie!! I know they don't have that much interaction in the game (or, uh, make that no interaction in the version of the game I actually played), but their personalities are so similar. It'd just be the sweetest thing, to me, for these two absolute beams of sunshine to come together across literal different worlds 🥺
I haven't finished the storyline of Legends Arceus yet, so maybe I'll feel differently at some point, but man, I immediately went all in on Akari x Rei (as player character and NPC respectively) from the first time they talked 😅
Probably my first ever Pokemon ship was Dawn x Zoey. It's been so long since I've watched the Sinnoh anime at all, but I've still held on to that one.
Also, I am (lightheartedly) disappointed in the lack of Pokemon x Pokemon ships in this thread! Some pairings that I've explored, from my teams in the games (because I can't play without making up whole personalities and stories for them) or just in general fannish ideas, include
*Roserade x Luxray
*Samurott x Seismitoad
*Gardevoir x Banette (It may be more subtle on Gardevoir's end, but because they are both ~spooky~ 👻 )
*Dracozolt x Aurorus
*Glaceon x Jolteon (My cringy childhood ocs 🥺)
*Trubbish x Yamask (...Too weird? I mean, they're in the same egg group 🤷)
*Manaphy x Diancie
*Uxie x Cresselia (See, more people ship Cresselia x Darkrai if we're talking about Pokemon pairings, but I feel like the embodiment of dreams x a personification of intellect and logic is just as interesting of an opposites-attract dynamic)
*Solgaleo x Lunala, but only when it's Nebby's parents 🥺