One of the best parts of a great anime series is getting to watch characters grow and develop into better versions of themselves. Sometimes, this growth can be pretty dramatic, to the point that the chracter is a totally different person by the series's conclusion. There's Izuku Midoriya from My Hero Academia, who goes from being a powerless middle schooler to a formidable hero (even though he still cries all the time), as well as Yona from Yona of the Dawn, who starts off as a spoiled princess but becomes a true leader who cares about her people. Many of the best anime characters begin as totally unlikable curmudgeons, but gradually become more endearing as they mature. Given how long some anime series go on for, it would be boring if characters' personalities remained static for dozens of episodes.
Izuku Midoriya — My Hero Academia
At the beginning of My Hero Academia, Izuku Midoriya has no special abilities to speak of; he's just a regular middle school kid. This is a problem, considering he wants to be a superhero and the vast majority of his classmates have superpowers, which they call quirks. When Izuku does get a quirk of his own, he has to endure a merciless training program and multiple encounters with villains before he's able to harness a fraction of its full potential.
While he still has a long way to go, he makes incredible progress in a short time, and can soon hold his own against villains.
At the start of Tokyo Ghoul, Ken Kaneki is a shy college student who loves literature and lives in denial of his familial issues. When he's attacked by a ravenous ghoul named Rize, the two of them get into an accident that destroys his organs, requiring them to be replaced with ghoul parts.
Suddenly, he craves human flesh, and finds himself embroiled in the underground world of ghouls. At first, he simply wants to ease into his new life with minimal trouble, but after being kidnapped and tortured, his personality does a complete 180; in light of the incident, he's willing to fight for what he wants.
Shinichi Izumi — Parasyte
After Shinichi Izumi of Parasyte becomes infected with an alien parasite, he's understandably horrified. He has no idea how to handle Migi, who has taken over his right hand, and all he can do is panic.
Eventually, he learns to work with Migi (rather than against him) to achieve his goals of defending humanity and keeping his deformity a secret. By utilizing teamwork, Shinichi is able to protect Earth from a parasitical onslaught, which would have been impossible at the start of the series.
Nagisa Shiota — Assassination Classroom
The primary focus of Assassination Classroom is class 3-E, all of whom initially seem weak and unmotivated, but achieve their full potential with the help of their teacher, Koro-sensei. As such, most of the characters experience polar attitude shifts, but the series protagonist Nagisa Shiota's is perhaps the most notable.
Nagisa starts the series off with no real direction. Due to a turbulent home life, he's depressed, and is performing poorly in school. However, when Koro-sensei — a tentacle monster with a smiley face for a head — becomes his middle school teacher, he and his classmates are challenged to assassinate the creature if they want to save the planet. The process of becoming powerful enough to actually kill their teacher sharpens him physically and mentally, and also helps him learn to work with others.