Gary Oak. Ash's rival didn't even show up for that many episodes during the course of their rivalry, having more impact on the plot after the rivalry was over.
The two Pallet Town trainers that went off on a journey alongside Gary and Ash are only given a couple brief mentions of their unknown journey, and are confirmed by the end of Ash's Kanto journey to have decided to just give up on their goal completely. Why these two were never seen before to interact with Ash, or act as a roadblock for Ash to eventually overcome to become a better trainer, is anyone's guess.
Any One-Shot Character of the day that leaves a major impact among the fanbase. Particularly, ones that are Ensemble Dark Horse status that fans wish would return somewhere down the line.
Any of the regional Evil Teams are always going to get the short shrift in terms of appearances, pushed to the backburner in favor of the usual Terrible Trio from Team Rocket. In the original series, this even extended to Giovanni and the greater Team Rocket syndicate.
It's odd that Bill, the guy who made the Pokémon transfer system, was a main character in many manga, yet has only appeared in one episode to date.
The champion of most Hoenn games, Steven Stone, only appeared in one episode of Hoenn with no reference to being anything beyond a typical hiker. You'd expect him to reappear later, but he never did. This contrasts sharply to future champions depictions and his game version, who has a major role. Thankfully, he returned in the XY Mega Evolution specials, and was involved in the climax of the XY series.
Pokémon that could/should have been captured by one of the main characters because they were either likable Pokémon by the fanbase or because their development with a certain character made it look like they would fit together with that trainer perfectly. Some examples being:
Haunter, Houndour, Larvitar, Hippopotas, Riolu, Scatterbug, Litleo, a shiny Phantump, and Wimpod for Ash.
Stantler and Sharpedo for Brock.
Swablu for May — this example is especially mean-spirited on the part of the writers, who had May care for the injured bird for an entire episode. When they finally tried to rendezvous with Swablu's flock, the flock was completely absent, causing May to offer to allow Swablu to join her team. The flock suddenly appears out of nowhere to prevent this.
Mightyena and Ralts for Max.
Grimer for Dawn. Another honorable mention for Dawn is that some feel it was a missed opportunity to not have her go after that one-off highly memorable evil Togepi. That way, the writers could build it up to eventually becoming a Togekiss rather than just outright handing Dawn a Togekiss a couple episodes out from the Grand Festival.
Deino for Iris, particularly because the owner of said Deino returned at the last possible minute.
Dewpider for Lana, doubly so given that the Pokemon's evolved form is her signature in the games.
While we're on the topic of Ash, pick a Pokémon from his roster that is believed to have gotten the shaft and watch it get ugly. Top choices include Pidgeot, Primeape, Kingler (after the Indigo League), Totodile, Torkoal, Torterra (after Turtwig evolved), Palpitoad, and Goodra.
The way Ash's Heracross was handled during Johto will definitely leave some people scratching their heads in confusion. Ash swaps out Heracross for Tauros to take part in a Tauros vs. Tauros competition, but when it was time to send Tauros back to Oak's lab once said event was done with, Heracross ends up not returning. What you're left with is Heracross not actually doing much since it was stashed away before the 3rd Johto gym battle, and doesn't actually appear again under Ash's command all the way until the league match against Gary.
Ash finally catches a member of a pseudo-legendary line (Gible), but the capture happened so late into the saga that very little was ever done about it. Most of the time Gible did have was spent on a particularly long arc mastering Draco Meteor.
After evolving up from Goomy, Ash's Goodra was only around for 15 episodes, and only appearing in a few of them, though it did a lot in those episodes. Its departure is a punch in the face to fans who were hyped about Ash finally getting a fully evolved pseudo-legendary. Though in the last case, he returned for the League.
Compared to how much mileage the anime has gotten out of Darkrai over the years, Cresselia received the short end of the stick. She only gets one episode, and even then she doesn't get to appear until the second half due to the first half being dominated by Team Rocket. And then Team Rocket comes back to hijack the plot again, and she spends the majority of her screentime as a Distressed Damsel who doesn't even aid in her own escape. The only thing she actually gets to do is confront Darkrai at the end of the episode, and the sequence takes fewer than thirty seconds. This would be weak representation for any Pokémon in the series, but giving this treatment to a legendary, and especially one that never gets a movie, not even appearing in the one starring Darkrai...
For the Episode N arc, Zekrom not being involved in any way has irked a lot of people. Mostly out of disappointment that Zekrom is now nothing more than a plot-device to restart Pikachu at the start of the Unova journey.
On to the topic on N himself, Ash's way of adventuring and his relationship to his Pokémon would have made him the ultimate foil to what he thinks is the average trainer and would have punched more holes in his logic even more so then Hilbert or Hilda (the Pokémon Black and White protagonists) ever could. Not to mention the ideological battle between Ash and King Plasma N would most likely would have been the greatest highlight of the entire series. Instead, N and Team Plasma are already in their Black 2/White 2 selves while Ash ended up hitting his dumbest point in the series.
Team Plasma simply being a generic evil organization in the anime annoyed many people. To be fair, this was how they were portrayed in Pokémon Black 2 and White 2, but the anime lacks the background of what they originally were in the first games and how that incarnation of the team got divided into the good side and the bad side, with only the bad side being portrayed.
Trip. Ironically, fans preemptively hated him because he showed early signs of being a second Paul. But then the writers started to expand his character. Half way through the arc though, it became apparent that the writers lost complete interest in him and focused more on all of the other rivals. Come time for the league, Trip became a total Anti-Climax Boss and got eliminated by Ash in the very first round.
Ash's Charizard, of all characters, became this during Black & White. He's added to Ash's Unova team (sending away Unfezant in the process) and rarely, if ever, has any interaction with any of the Unova Pokémon outside of Iris' Dragonite, whose rivalry with him ends as soon it is introduced, and Ash's Pignite, who N states they already have a good friendship but otherwise show the same concern for each other as they would with other Pokémon. They may has well have had Ash send Charizard back to regain Unfezant.
During Diamond & Pearl, the writers made the mistake of trying to cram too many rivals into Dawn's Contest arc. As a result, Ursula's conflict with Dawn, as well as Nando's decision to pursue both Gym Battles and Contests, were never explored in depth because of their lack of screen time (and many opportunities to do so were wasted in favor of irrelevant filler).
Connected to Dawn's Contest arc, there was also Lila, a Pokémon Coordinator that served as Dawn's main opponent for winning her third ribbon. Lila was someone who already had four ribbons, and has a major connection to Dawn's family being her mother's primary rival in the past. If her match against Dawn was used as a means to reignite her passion for Contests, all Lila had to do was win one more ribbon at some point, and could have made further appearances as a competitor in the Sinnoh Grand Festival. However, in the end, Lila stayed as a One-Shot Character.
While the female protagonists are usually lucky enough to get plenty of focus, the male protagonists of their respective games tend to get screwed in that regard due to the show's strict focus on Ash. If they're lucky, they might get a cameo in a movie, but many viewers who view Ash as The Artifact are dismayed with the anime's refusal to replace him.
Sun & Moon sees Ash having his largest group of friends yet with, including him, a group of six. However, it seems clear that the writers either have their favorites or simply can't handle that many characters at once. As a result, some of them tend to be Out of Focus. One of the worst offenders is Mallow who, after her Bounsweet evolved into Steenee, seemed to have been left aside, not having much Character Development and being the only of the Akala trio not to have Z-Ring, as the Grass Trial was taken by Ash so that his Rowlet could have a Grassium Z. Sophocles doesn't fare much better, either, having little more Character Development than Mallow in spite of having more episodes focused on him than she does. While Lana and Kiawe fare better, they're both outshined by Lillie, who is the only one to receive a fair amount of presence to the story as the Deuteragonist.
It takes awhile for Team Skull to show off any real importance other than being just a mere nuisance to the main cast. While many in the games saw the Team as such, the anime almost makes them look like total pushovers who were Demoted to Extra compared to their game counterparts, with most of the stuff they would be expected to do done by Team Rocket instead. It doesn't help that, even after two years of the Sun & Moon series and both Motherbeast Lusamine and Necrozma received arcs in the series (the former of which happened without their involvement), it took until episode 115 for Guzma to finally appear. The fact that Plumeria's long awaited debut only happened in episode 104 of the series and consisted of only appearing for a few seconds without being named or doing anything only fanned the flames further for some fans. And when Plumeria finally does battle in the Alola League, she is quickly eliminated by Ilima in the preliminary round.
Hau, the main rival of the Sun & Moon games, is another example of Demoted to Extra, with Gladion instead being Ash's main rival. Like Guzma and Plumeria, Hau was introduced really late into the anime (episode 97), and ends up with a total of just one episode to build up his character before the start of the Alola League, which is when he finally reappears again. What you're left with is Hau coming off as just an unimportant One-Shot Character that was lucky enough to make a comeback for the league.