Aureliashipping. If you ship it, you do you. If you like S/M and Lillie enough to like this one, I promise our sensibilities are opposites and that's okay. It's nothing personal.
What is an issue for me, though, is that this dynamic kinda falls into the general Lillie Problem in her home series: basically every other character exists in service to her. (FWIW there are scenes where Lillie is there for Ash, but the most prominent one is in an episode I despise, with the "Rotom goes away" ep.) Also, she's just generally too mellow for me. I don't like shipping Ash with softer, low-energy characters.
Pokeshipping. Poke is a weird one for me. I 100% think the ship is canon! I think it's pretty textual that Ash and Misty held feelings for each other, bare minimum, in the original series. And I like it! It's charming. My thing is that I just don't see the chemistry when they're adults and more mature than they were when they were kids.
I see them as each other's first puppy love. They joke about it as adults, and even flirt playfully. But, they tried dating in my AU, and found they went together like Water and Oil. (Shameless fic plug!) They're essentially each other's best friends, and can call on one another in the middle of the night if they need literally anything. Just like, as friends.
Pearlshipping. I kinda flipflop on this one, since I have a few OTP-tier ships. But this is really The One if I had to pick one. I've shipped it since early D/P, and I met my wife through it. Wrote my magnum opus centered around it. Ash and Dawn's buddy-buddy energy is infectious; they care so much about each other!! They make each other stronger and borrow techniques from each other! They yell at people in defense of one another! They have High Touch!! They are goals! I see them as soulmates. (Though, I personally believe they have several of those.)
My second choice pairing for them
Three-way tie between Amourshipping, Pikashipping, and Chikoshipping. Amour is just really cute, and shares some of Pearl's positives. I also met one of my best online friends through it. I have a soft spot for Amour and feel the need to go to bat for it often.
I considered putting both Pika and Chiko in the OTP spot; the four of these honestly could fight for it. I love the idea of Ash and Pikachu/Peeks being soulmates; both platonic and not. Cyaneko's art reawakened my childhood love for the ship. I love the idea of Ash's starter being super affectionate and possessive of him. I like the idea of them kissing when no one's looking as Peeks rides on his shoulder. Love the idea of them using each other's petnames: Buddy/Pikapi.
I'm also extremely weak for Ash and Bayleef, and have been for the past year or two. Their earnest, straightforward chemistry and affectionate is just to die for; it's adorable. I think Bayleef's earnestness and stubborn nature suit Ash perfectly, and it makes her a great life partner for him. I can imagine them just going on adventures together, like Ash with Pikachu/Peeks. I'm a little obsessed with it, right now!
My fluffy pairing for them
Altoshipping. I think their fairy tale romance from Heroes is just to die for. They're so playful in the movie and I can see them maintaining that energy forever, when they reunite. I love writing fluff with them.
My angsty pairing for them
DeepBondshipping, is apparently the name for Ash x Greninja. (I found this on a ship wiki under "friend ships," but fuck you, it's romantic.) While their ultimate outcome is a happy ending, I see it as somewhat angsty during XY, where a very self-obsessed and disciplined Froakie sees a glimmer of love in Ash, and chooses him to draw out his power... but over the course of their journey, he begins to feel rejected. Ash can Mega Evolve his Butterfree with ease, and even that Hawlucha, whom he's always butted heads with. Why is it so easy for them, but their transformation so hard for him!? Greninja sees their struggles, and Ash's hesitation to use the form, as a wholesale rejection of his mission and their love, and turns cold. He and Ash struggle to communicate, leading to the slowburn of a fracture between them in the Ash-Greninja arc. Ash's budding romances with his friends and partners around him deepen Greninja's feelings of rejection; something he's not even properly conscious of. It all comes to a head after they face Wulfric.
They experience each other's internal turmoil through a trial by a friend of Wulfric's from the Unknown Dungeon, near Pokémon Village; an entity of absurd psychic powers who recalls Ash from his own past. Through his trials, Ash and Greninja come to understand one another, and master their form; confessing their turbulent feelings after the fact.
It's a relationship that suffers a fair bit of strain, before it's mended and perfected. I also just think the idea of two people who literally share bodies and souls is incredibly intimate and ripe with shipping potential.
My favorite poly ship for them
God, I have a lot of these. Amourinterditshipping is probably my go-to! I see Ash, Dawn, and Serena as a proper throuple; so much so that I had them married and living together, before deciding to let them live their own separate lives. They all work to uplift and balance each other out, and have enough in common to work as a trio, more often than not!
My weirdest pairing for them
I kinda ship him with Movie 8 Mew; don't really have a name for it, as of now. It's one of those "mortal x immortal" ships, where said immortal sees the former as their favorite lil' plaything. Mew recognizes Ash mostly as Sir Aaron, from the time they'd spent together in a past life.
So, when Ash returns as a proper adult, Mew likes to amuse herself with his presence, and drop by at her leisure. One could almost consider Mew caught, but truly, it's more like Mew caught an Ash...!