Jessie, James, and Meowth. Though they're not without their sympathetic qualities, many fans ignore their clearly unsympathetic actions, like trying to steal a 10 year old's best friend, trying to kill people who get in their way, harming or even attempting to kill Pokémon who've pissed them off (they nearly killed the Squirtle Squad with homemade bombs and they clearly weren't planning on letting the Scythers who gave Jessie a new haircut walk away), trying to kill a 10 year old on several occasions, etc.
Parodied with Meowth of Team Rocket. He has this with Giovanni, even though Giovanni frequently mistreats him and is shown to be ruthless. Meowth imagines him as simply a nice guy with a gruff exterior who likes to go shirtless. He also sees himself as competing with Giovanni's pet Persian for attention, although it's clear Persian couldn't care less.
Before Garys HeelFace Turn when he was still a jerkass, fans tended to take his side over Ash during the Kanto/Johto arc of the show by justifying his jerkass behavior towards the latter. This is due to the fact that Gary was always one step ahead of Ash. This is also because he was a well skilled trainer that earned 10 badges while Ash didnt earn 4 of the 8 badges that he had correctly. While Ash had his flaws and was Not So Different, fans are ignoring the fact that Gary was much more arrogant and rude than Ash ever was in the series and that Gary was knocked out of the Kanto league earlier than Ash did.
Paul is easily the biggest Jerkass among Ash's rivals, releasing any Pokémon that don't meet his standards, insulting Ash at any given opportunity and acting cold toward everyone else he meets, and most notably having his entire team gang up on his Chimchar in an effort to force it into activating its Blaze ability (which is unusually powerful) and then rage-quitting on it and releasing it, effectively abandoning it out of disgust (everything that happened that day and the night before really soured Ash's opinion of Paul). Despite his jerkassery, he has a sizable fanbase that are willing to ship him with Dawn.
Harley is often softened up because he's extremely popular and over-the-top, to the point that James even said he wore leather pants in the PUSA Dub. His sheer flamboyancy garners him quite a fan base, even if in-universe, most attempts at being pleasant are purely manipulation to fulfil his vindictive (and hard to define) obsession with destroying a ten year old girl.
Georgia is more of a downplayed version since she's only a rival who engages in petty squabbles with Iris (and she admittedly does get better later in the series). Fans tend to defend her rude behavior towards not only Iris, but to everyone else on the show. They tend to forget that Georgia acts more immature and practices poor sportsmanship, and that her role is The Rival in the series.
Cyrus from Pokémon Diamond and Pearl/Platinum has quite the fanbase due to his sympathetic backstory... despite the fact that he tries to destroy the universe and re-shape it using a Legendary Pokemon (Either Dialga, Palkia, or both depending on which version you get) so that he can basically become God. In Pokémon: Diamond and Pearl Adventure! he manages to redeem himself, starting from when the hero shows compassion towards him. This series is hugely popular among his fans and Team Galactic fans in general, partially for the more humanised view of the members, though even then it's made quite clear that they're wrong in what they're doing.
Silver, The Rival from the second generation, gets this a good bit too; he's easily the biggest asshole of the rivals in the series (what with Blue basically just being kind of a brat and petty bully, and the others all being friendly), between stealing from Elm, kicking/punching/shoving you in what is one of the only direct acts of violence from a human in the series, and infamously stripping you just when you were about to infiltrate a building infested with Team Rocket members, but yet he is one of the most popular and loved within the rivals. However, unlike some other examples it can be justified if the fanwork depicts him in the later parts of or after the events of the game, as he does get a HeelFace Turn and majorly takes a level in kindness by the end. It helps that he, in the remakes at least, has one of clearest character arcs and Character Development of any rival, has a Freudian Excuse in being Giovanni's abandoned son with a major Inferiority Superiority Complex thanks to it (quite possibly the primary reason for his popularity), acts like a Tsundere towards the end, becomes a borderline doting trainer and has nothing but humble respect for you by the end, has much more of a pretty boy look, and for the less emotional side of the fanbase, the fact that he's such a badass, that people tend to love him. It should be said that when he is discussed, even fans of him almost unanimously agree that he was an unrepentant JerkassHate Sink initially.
Generation I/III Blue sometimes gets this as well; while he isn't evil by any means, some, especially in the Japanese fanbase, make the mistake that relations between him and Red were perfectly peachy when manualsshow that to not be the case, or tone down his Jerkass qualities despite him being infamous for them. On the western side of things this can get particulary bad with people who believe that his Ratticate died on the S.S. Anne (some going as far as to give Red the Ron the Death Eater treatment), along with some people treating him as a bit of a Memetic Badass, probably in large part due to the reputation of his anime counterpart and being the Final Boss. His more mature Older and Wiser teenage self in the second generation and their remakes, and a Bishounen look in the latter (and to a lesser extent in the first generation remakes), do not help matters.
Giovanni himself gets this too, due to him being a rather handsome Yakuza/Mafia crime boss with nice clothes to boot. In the Japanese fandom this can be seen with the Rocket Executives as well; though they are still acknowledged as evil, they often get turned into more comical versions of themselves like a somewhat more competent version of the Team Rocket Trio, get their Undying Loyalty (especially Archer) to Giovanni played as a Tear Jerker, or both. Note that these are a bunch of Pokemon traffickers, thieves, and murderers, but damn if Archer isn't loyal to his former boss. This may be at least partially attributable to the anime due to aforementioned Terrible Trio.
N may not be a villain, but most fans forget that he was explicitly built up as the main antagonist in the first game, and intentionally antagonized the main character into conflict in most of their meetings. The fanbase's utter adoration and ignorance of his bad qualities, especially when Black and White was still new, is probably why Pokémon Adventures decided to make him muchlesssympathetic and amp up the "Jerkass" in Jerkass Woobie. However, unlike many other examples and similarly to Silver above, this isn't without basis in canon due to most if not all of his bad actions purely being the result of him being misguided by Ghetsis and his Ambiguous Innocence, with it being shown that the man only ever had good intentions, and by the end of his Character Development he becomes much more of a straight-up hero.
Lysandre sometimes gets this as well; it is not uncommon for fans to downplay his actions, even depict him hanging around with the main characters, despite the man being completely Zubatshit insane.