Do you love anime characters who get really, really enthusiastic about their favorite thing? Then you probably like anime characters who are fanboys.
Anime fan boys aren't always boys - they're people of any gender who are totally obsessed with a person, topic, or piece of media. Sometimes, these obsessions can be endearing, but other times, they can come off as creepy or overbearing. How is this different from fangirls? Fangirls are also obsessed with their subject or person of choice, but it plays out differently. Think, knowing all the trivia about your favorite idol versus shipping them with all of their bandmates, and you have the difference between fanboys and fangirls. Not to say that fanboys never have romantic or even sexual feelings toward their subjects, or that fangirls don't know a whole lot of information about them, but the overall focus is different. Are these definitions based on gendered stereotypes? Totally, but it is what it is.
There are examples of these characters in everything from shonen series like One Piece and My Hero Academia to slice of life shows like Princess Jellyfish. Which ones are you a fan of? Be sure to vote them up!
Ever since he was a little boy, Izuku Midoriya has been totally obsessed with superheroes - especially All Might, who is widely recognized as the world's greatest hero. His dream is to be accepted into U.A. High School and become a hero himself. That dream seems completely out of reach until he impresses his idol during a chance encounter, and ends up becoming the heir to his powerful quirk.
Once Izuku is well on the road to becoming a hero himself, he still retains his obsession with all things hero. He also continues to idolize All Might even after he gets to know him as a person.
Zoe Hange is one of the few non-male examples on this list. When it comes to Titans, they turn into a total fanboy. Sure, they want to know everything there is to know about the creatures in order to properly deal with the danger they pose to humanity, but that doesn't explain their rapturous excitement at the idea of performing experiments on them. Most other members of the Survey Corps see Hange's obsession as weird but still respect the skill and expertise they bring to the group.
Ever since he met Luffy in Loguetown, Bartolomeo has been absolutely obsessed with him. Not only does meeting Luffy inspire him to become a pirate himself, he also has a ship that looks almost exactly like Luffy's ship, Going Merry. He even calls it Going Luffy-senpai, a nod to both the ship's name and to the person he worships.
It might seem like a bit of a dismissal to call Teru Mikami's obsession with Kira fanboy behavior - but it's also pretty accurate. At first, Mikami is obsessed with justice in general - a reasonable preoccupation for a prosecuting attorney, but he takes it to the extreme. When he's approached by Kira to participate in his plot, Mikami's obsession with justice expands to include Kira, the "god" he dedicates his energy to serving.
He gets so into writing names down in the Death Note that he literally looks like he's having an orgasm - if that's not an obsession, nothing is.