Watching static anime characters go through a new adventure each episode makes for a relaxing, if safe, viewing experience - who doesn't have a soft spot for Ash Ketchum? But when it comes to characters who truly stick with you, they tend to be well-developed anime characters: protagonists and supporting characters who change and grow over the course of a series. Anime characters with great development arcs add another reason to engage in a particular movie or series. Sometimes, even a supporting character surpasses the protagonist with a more compelling arc than the man character's.
Such characters undergo major changes in their personalities, approaches to life, and their relationships, emerging as different people by the finale. Anime characters with excellent character development appear across genres. You might remember Dragon Ball Z as a mindless fighting show, but Vegeta exemplifies the change from villain to hero by the end of the show. Great development also occurs in more realistic storylines - Seishuu Handa goes from an anxious workaholic to a relatively well-rounded person over the course of Barakamon.
Sometimes, it's not the journey or the destination that make an anime great, but the characters who carry you through them.