There are scores of villains in My Hero Academia, which makes sense given that the world is heavily populated with Quirk-carrying humans, enough to outnumber the Quirkless four-to-one. The story makes it a point to explain that villains are as bound to their circumstances as heroes, meaning that many of them are not entirely irredeemable.
Disregarding most small fry, there are a few villains whose life journeys and personal aspirations carve their paths out in ways that audiences can appreciate and respect. Fans abhor antagonists like All For One, a combination of incredible smarts and overwhelming greed who seems to have no conceivable path toward redemption, but "evil" is not necessarily hardcoded into everyone else.
Tomura Shigaraki
Tomura Shigaraki is far from being a fan favorite, but his popularity has been increasing ever since he inherits All For One's quirk. This closeness to One For All, as well as his troubled past, forms the crux of his complicated character arc. Interestingly, Tenko Shimura is his real name, and his pseudonym is granted by his master. Before his transformation into the villain he is currently, Tenko shares an adorably similar feature with Deku, that being an intense fascination for all things hero.
Tenko ultimately kills his parents and sister when his Decay Quirk goes haywire, and the rest is history—except it's not. Deku has, in recent manga chapters, claimed that he would do everything in his power to "save the little boy" hiding behind the layers of rage that Tomura uses to shield himself against human connection. Deku's defense of Tomura has rubbed off on both his predecessors and fans of the show, as it strongly suggests that the so-called villain might just get a chance at redemption.
Twice
Jin Bubaigawara, also known as Twice, is a hilarious character, forming the comic relief facet of the League of Villains whenever a light atmosphere is needed. He thoroughly endears himself to the audience by means of his bizarre antics and campy mannerisms, and he's playful as he is outlandish. Twice firmly believes that every person has a firm grip on their identity, but his mega cloning extravaganza forces him to confront the nature of his own reality.
This metamorphosis is rooted in the true meaning of his Quirk, considering that Twice clones himself just so he can have someone to talk to. Most people can relate to his experiences of loneliness, given that many have had childhood imaginary friends to keep them company. Villain or not, the man is undeniably intelligent, and charming, in his own whimsical way, but it is the emotional pain he endures that makes him an appreciable character.
Dabi
There is an ocean of differences that separates Dabi the villain from Toya Todoroki, the firstborn of Enji—better known as Endeavor. While the adult version is a ruthless monster, the formative events in his past provide some important context regarding his descent into villainy. Endeavor, in his bid to "create" offspring capable of fulfilling his dreams for him, foists an unreasonable amount of pressure on young Toya, a decision that results in failure.
However, the boy refuses to accept his limitations and continues training to prove his naysayers wrong, a stubbornly charismatic characteristic of many popular shonen protagonists, until he apparently perishes in a fire of his own creation. During the Paranormal Liberation War arc, Dabi discloses his father's cruelty on public television, leaving the latter with no choice but to acknowledge his responsibility. Endeavor might have come clean about everything, but the "leak" has convinced fans to consider Dabi in a far more positive light.
Gentle Criminal
Gentle Criminal's storyline in My Hero Academia revolves around casual villainy in that he doesn't exactly have a grandiose vision like Tomura Shigaraki or Kai Chisaki, but that doesn't mean he doesn't cause any problems. He is eerily composed when faced with opponents who are undeniably stronger than him, which makes Gentle Criminal significantly more likable than many Pro Heroes even.
Further, the amount of affection he displays for his sidekick, La Brava, describes the man's path in life as a result of his circumstances, implying that he still has a chance to redeem himself. This is why Deku struggles with all his might to show Gentle Criminal that violence isn't the answer and that criminal notoriety isn't one of the better methods to gain more online followers. Audiences love this villain's personality, as it ranges from immaculate & and courteous to downright whimsical.
Kurogiri
Kurogiri's immovable dedication to All For One's violent vision makes him a cold-hearted antagonist and one of the more malevolent entities in My Hero Academia. He is known to have zero moral compunction when it comes to fighting, often forcing children into perilous and potentially fatal positions. As such, Kurogiri is not very appealing to audiences, but it's a completely different story after his past is revealed.
Apparently, All For One swipes the corpse of Oboro Shirakumo, one of Eraser Head's beloved childhood friends, and works alongside Dr. Garaki to create Kurogiri. The latter is probably the first successful outcome of the Nomu project, adding a completely new dimension to his character. Oboro's altruism is vaguely visible through Kurogiri's hostility, convincing fans of the show to appreciate the multitudes within the villain who is severely limited by the brutality of his experimental programming.
Himiko Toga
Himiko Toga's Quirk has menacing undertones, not only because it allows her to copy people's appearances, but because she needs to drink their blood in order to activate Transform. Nevertheless, it is clear that Himiko grapples with her understanding of both the world and her place in it, which goes a long way in explaining her sadomasochistic habits.
While she attempts to learn about other people in order to make the most of her Quirk, it almost seems like she's genuinely interested in her targets. Even fans who dislike her character intensely can't help but acknowledge that Himiko, at the very least, is deserving of sympathy for everything she has had to endure in her short lifetime. In other words, it's rather difficult not to commiserate with Himiko's emotionally devastating experiences.