How Much Do You Think Ash Remembers?

He remembers if the plot requires him too. Otherwise, when he travels to a new region he starts over with a blank slate, just Pikachu as his 'starter'. Though Pikachu seems to stay strong every time.

I honestly think that he remembers a lot more than most give him credit for. But it's played down enough it's not blatantly obvious, so as to not overwhelm the casual viewer.

I'll give a few dub and sub examples.

First of all, in the Dub of the movie with Mewtwo and Genesect, when he first see's Mewtwo he begins saying, "is that.." obviously recognizing the form until the female voice interrupts him (probably leaving him just as confused as the rest of us). But I'll save an explanation for the rest of Ash's encounters with legendary Pokemon for a separate post, as it's based on an admitedly very particular headcanon of mine :P.

Spoilers ahead for Pokemon Sun & Moon, but these are the best and most obvious examples I can think of off the top of my head. In the Episode where he battles Hala, he pretty much uses the same exact strategy to beat his Hariama has he did in Hoenn against Brawly. Nobody says anything about Hoenn or that Ash has even used it before, it's just 100% on us, the viewers, to understand the connection.

XY had an impressive amount of continuity in Ash's battling skills as well, albiet without explaining it themselves very well. In his first gym battle Ash was faced with an Ice battle field, which many say is something that Ash should know how to deal with. However, they are missing a crucial detail; Ash has always dealt with Ice battle fields by ricocheting off of rocks. There were no rocks this time. (Credit to TyroneTheGod of YouTube for noticing this one)

And then there's team Rocket. I'm pretty sure Ash always suspects Team Rocket for everything at this point, he just doesn't voice it. Disclaimer: I'm going off of fansubs here. in the episode "Shocking! A Dugtrio Split-Up?!" Of the Sun/Moon saga. First, let me explain the scenario. Team Rocket convinced DJ Leo's Dugtrio to quit on the DJ in order to join their own "really Famous" band. At first, Ash seems to naively believe that the "really famous" band scenario was legit (like everyone else), and convinced DJ Leo to go find Dugtrio under the grounds of convincing Dugtrio to give him another chance. Ash offers to help find them... and then he does something really strange.

For some reason, having Rockruff sniff out Dugtrio's scent, is the method of choice for seeking out this "Really famous band." Then, when they do indeed find Dugtrio with Team Rocket in a nearby rundown shack, Ash apparently says something to the effect of: "I knew it was you". Either I and the fansubber are smoking somethin or Ash suspected Team Rocket the whole time.

hmm...

Movies: Totally erased from his mind

Older Season: Only vague memories of his friends, most likely forgotten all of his other pokemon stored in the Oaks ranch.

Serena's kiss: Just a fever dream and thinks that it never happened.

Only thing he does remember is his army of Tauros... XD

I'm just gonna go with "Ash remembers zilch since every region sees a new Ash start on his journey" makes my head hurt less than seeing the same Ash who just toppled a god get his butt kicked by a new trainer

As I said before... Satoshi (Ash) is a timelord that dies and regenerates after the start of each new series.

That would explain his battle strength and slight change in personality XD

Nope, he is just a straight out dumb kid who cant remember any dumbsh*t so don"t worry if he forgets all his adventures and classmates in the next series.

Ash couldn't remember how many fingers he has. Basically, after every series finishes, Ash scoops his brain out of his head, squeezes it dry like a sponge, takes a little bite out of it, then tosses it back in. That's also why he always wears a hat outside FYI.