For quite some time I have had a penchant for characters that exhibit Zen-like or Buddhist qualities. Perhaps it’s their cool demeanor in the face of danger that allures me, but it’s hard to say. But what qualities are “Zen-like” or “Buddhist”? Wikipedia names these qualities as having mindfulness and concentration for Buddhism and Zen (since Zen is a school of Buddhism), and an “emphasis on experiential wisdom” .
In the landmark movie Ghost in the Shell, the character embodying these qualities is certainly Batou . He is always mindful of his surroundings and of those around him, even when those around him aren’t. A key example of this in the film is the following part of the film upon the team’s capture of the Puppet Master:
Kusanagi: Don’t let anyone else dive in there before me!
Aramaki: What’s with her?
Batou: l wrote in my team evaluations that she’s been acting weird ever since this Puppet Master case fell into our laps. Do you even read them?! 
Aramaki, who is portrayed in the series and movie as usually being acutely aware of his surroundings, is completely unaware of Kusanagi’s struggles with the Puppet Master case. The same goes for most of the other characters (although most of them are too occupied with their own problems to notice Kusanagi’s) except Batou. Although he is not able to control the outcomes of the situations that he ends up in (contrast with Kusanagi in the second film, Innocence), for most of the series he remains mindful of his surroundings, rarely off guard, and under control.
An important aspect of Zen is the relationship between the teacher and the student, which is epitomized in Ghost in the Shell between Major Kusanagi (the teacher) and Batou (the student), notably more in the second film, Innocence. Throughout all the Ghost in the Shell works, however, Batou is consistently second-in-command to Kusanagi and her right-hand man. He is an unlikely student, as he is already confident in his world view. Yet he is always listening to Kusanagi, open to her ideas, and open to discuss anything with her, a relationship that no other people enjoy in the series or movies.
Kusanagi becomes the teacher even more once she becomes one with the Puppet Master at the end of the first movie, gaining greater intelligence, access to new parts of the ‘Net, and a revised outlook on the world around her. She watches over Batou throughout Innocence, subtly warning him when he is in danger. Her greater abilities and similar mindfulness of her surroundings allow her to do great good for Batou and his mission, showing that they are both symbols of Zen in anime.
Zen is something very difficult to quantify, but in a very Batou-like way, I would say Zen is the following meme:
“Perfection is right in front of you, just open your damn eyes and see it.”