Ash, Pikachu and Team Rocket. Because they are the most prominent characters in the show, they do have a following among regular watchers of the anime, and their depictions in early seasons tend to be quite popular. However, it's very common for fans to label them as annoying, ineffectual and seemingly tailor-made to entertain young children and nobody else, with Flanderization and Adaptation Displacement not helping matters.
Ash's skill as a trainer and characterization has constantly been in flux throughout the history of the anime. The fans have been critical of this, citing that they can easily use the game characters to both avoid the predictable, drawn-out nature of Ash's journey where he goes from being incompetent to skilled over the course of the series. Those who don't see him as The Artifact say that Ash is far too iconic to be replaced. In particular, Ash's XY incarnation is a strong example of this; while most fans agree that his battling record during the Kalos saga was at its best, some also feel that it made him a strong and likable character in the first place while others feel that he was too dull, bland and uninteresting as a person. Sun and Moon tried to form a balance, giving him a more expressive personality while maintaining his battle competence for the large part, but the depiction remained very divisive as his character appeared to change each episode (ranging from The Ace to Butt-Monkey) whenever a situation deemed it and Depending on the Writer.
Pikachu splits the base in almost the exact same fashion as his trainer, being inconsistent in both character and power. Some abhor Pikachu for being a Spotlight-Stealing Squad in and of himself, being slapped on every piece of merchandise, and/or refusing to evolve. Others praise and respect Pikachu as the Japanese equivalent to Mickey Mouse while finding him genuinely cute and entertaining.
For Team Rocket, depending on who you ask, they are iconic as comical Harmless Villains who are more entertaining than Ash himself, or their incompetence and sideplots in an episode are overdone and just plain annoying. In addition, the fanbase is also left divided over whether Team Rocket was improved as characters after they Took a Level in Badass and start becoming serious villains. There's also another group who remains unconvinced that they've taken any such level at all. Their portrayal from XY onward has tried hard to appeal to all sides of the argument, though alas they're so divisive, it's impossible to please everyone in this regard.
Brock was a generally well-regarded character in the earlier parts of the anime, but the persistent Running Gag of him falling in love with every young woman he sees was either funny or tiresome, particularly by Diamond and Pearl.
Cilan. Either he is a better character than Brock and his strong personality is refreshing, or he's getting too much focus, has gotten as stale as Brock was as a result, and is a spotlight hogger for those who find him and his antics "forced" or "overexposed".
May. She's either an improved version of Misty with more focus on her nicer aspects, or the attempts to replicate her tomboyish nature get her viewed as inferior to the original. However, the negativity surrounding her replacing Misty largely subsided once Misty appeared with her and they become friends.
Dawn is either loved for being the likable Nice Girl, or viewed as a generic Suspiciously Similar Substitute to May due to their contest plots. Some even called her out for being too different from May.
Iris received a substantial amount of flak for her constant habit of referring to Ash as a "kid". She was also criticized for bucking the trend of a female protagonist as a traveling companion. Others found her unique quirks and Character Development interesting, and like the fact that she was another attempt at a female companion trying to master a Pokémon type. Then there are those who see her as a case of They Wasted a Perfectly Good Character.
Lillie. On one hand, there are those who don't like how her well-loved character arc (and all things attached to it) from the games was removed, while others enjoy the fact that the anime is taking its own liberties with her character, such as her character arc regarding her phobia of touching Pokemon and many episodes punctuating her role as the AdorkableSmart Girl of the group. The fanbase was further split by her treatment in the Aether arc for losing all her progress and gaining it back with no work of her own and calling out her well-meaning mother for no reason. That she got more focus after that while her fellow cast members struggled to get any made her seem somewhat of a Creator's Favorite as well.
Mallow, Lana, and Sophocles all get this to some extent. This is mainly due to the fact that in contrast to previous series, which would just have a main cast of 3-4 people, Sun and Moon has a cast of six to take care of. Some find this refreshing, enjoy all of the different characters' quirks and dreams, and feel that it allows for a much more diverse and varied cast. Others, however, dislike the uneven limelight, with the three in particular criticized for their stagnancy, and sometimes considered less interesting characters than the more dynamic trio of Ash, Kiawe and Lillie who have whittled focus as a result of their presence. By Ultra Legends their reputation calmed mildly due to an improvement in limelight episodes and breakthroughs as trainers, though some still regard them as dead weight and less interesting protagonists.
Gary is typically a Memetic Badass, but you will often find people who view his tormenting of Ash as extremely overdonenote As an example, in Beauty and the Beach, despite having not even run into Ash once since the first episode - in which Ash was very cordial with him despite Gary's snide comments - he proceeds to get on stage and publicly mock Ash, even getting his cheerleaders to sing about how he'll trash him; plus his famous sign vandalizing to declare "Ash is a loser" even earlier, especially if they've dealt with similar bullying experiences themselves. After he Took a Level in Kindness, people either found him now boring without his Awesome Ego, or much more tolerable.
Ritchie either serves as a good Foil to Ash, or is a blatant shallow sue.
Paul. Some fans hate him, feeling like he got too much love from the writers and was an accurate representation for Stop Having Fun, Guys and Munchkins, and never received any proper karma for his massive jerkassery. Others took a liking to him because he is a Strawman so Anvilicious that it's hard to seriously see him as such an accurate representation of competitive players, or are sympathetic to Paul because of the few things that are accurate to said players and his criticisms of Ash (usually considered an Idiot Hero). He's also a popular candidate for shipping, particularly with Dawn.
Barry is seen either funny or annoying.
Sawyer is seen as having rushed development by some. Others say his development was paced just fine because he doesn't have Team Rocket following him and all the Filler episode characters, and had Ash as a mentor. There are also those who wish Sawyer would have developed more evenly, but are happy with how he was given time constraints.
Good lord, Alain. Specifically, his involvement with the league is either seen as perfectly natural Character Development or a massive Ass Pull. After he beat Ash in the league, the base divided even more, all of it concerning if Ash should of won thanks to the buildup.
Lusamine, again based upon comparisons to the games. Some people love her Adaptational Heroism, quirkier personality and the bond she has with her family, while others who feel it downplays the games' first female Big Bad and one of the most twisted villains the series has ever had. Basically, the division comes down to how the anime handles Lusamine as a character as a whole vs. Lusamine as a villain. The fact that that Faba took her place as main antagonist is also a point of contention for some, citing that we'd already seen manipulative schemers like him before with Cyrus, Colress and Lysandre. Then there are fans who are outright angry that the first female main antagonist of the games was the only one shafted in favor of another character.
Iris' Dragonite. Legitimate Badass, or a poor clone of Charizard's story that gave Iris undeserved victory?
Ash's Poipole. One half of the fanbase finds it positively adorable and love his antics, his budding friendship with Pikachu, and his teased plot relevance with a possible connection to Necrozma, with many hoping Ash will get to keep it at the end of the series. The other half hates him for his bratty behavior and for not having done much since its debut, with perceived similarities to Nebby and being one of Ash's main team members without contributing to battles being used as accusations against it.
Also similarly, the Shaymin adopted by Mallow. Some love it for its cuteness and Nice Guy personality (compared to the Bratty Half-Pint Shaymin of Giratina and the Sky Warrior) and acting as one of the more stagnant companions de-facto secondary. Others complain about Shaymin not really doing anything besides acting as The Baby of the Bunch and feel that Mallow is undeserving of possessing a mythical Pokemon.