Here are some notable AI characters from Japanese anime, along with a brief description of what they can do:

Sibyl System from Psycho-Pass: This AI system is used to monitor the mental states of citizens in a futuristic Japan, determining their potential to commit crimes. It uses a network of scanners for surveillance and even influences job assignments and political elections. Its core consists of human brains, making it a unique blend of human and artificial intelligence【44†source】.
Gantz from Gantz: This mysterious AI controls a high-stakes game where participants, after their death, are forced to fight against alien and robot monsters. Gantz provides equipment and instructions to players and has god-like powers and control over the game’s technology【45†source】.
Love Machine from Summer Wars: An AI released into a massive social network called OZ, Love Machine causes chaos by stealing user accounts and gaining control of various systems, leading to a potential global catastrophe. It’s characterized by its ability to adapt and incorporate other avatars, displaying a sadistic personality【46†source】.
Agumon from Digimon Adventure: Agumon is a Digital Monster (Digimon) in the Digital World, partnering with a human named Taichi “Tai” Yagami. Agumon can evolve into different forms and exhibits a brave yet laid-back personality. It represents the blend of virtual life-forms and AI in the Digimon universe【47†source】.
Ritsu from Ansatsu Kyoushitsu (Assassination Classroom): An AI from Norway, Ritsu’s body is a rectangular box filled with weapons and a 3D printer. Initially robotic and emotionless, her personality becomes more cheerful and friendly after modifications, enabling her to interact better with her classmates【48†source】.
Aura from .hack//SIGN: Created to be “the ultimate AI,” Aura plays a central role in the .hack multimedia franchise. She’s designed based on the daughter of a genius programmer and is kept asleep by another AI, Morganna Mode Gone, to prevent her awakening from rendering Morganna obsolete【49†source】.
Chamber K6821 from Suisei no Gargantia (Gargantia on the Verdurous Planet): Chamber is an AI within a mech body assisting the protagonist, Ledo. It shows high intelligence and autonomy, helping Ledo navigate a new world after being thrown into space. Chamber’s personality evolves alongside Ledo’s, showing a development towards full sentience【50†source】.
Rundellhous “Rudy” Kode from Log Horizon: Rudy, an AI character from a fantasy MMORPG, tries to emulate human adventurers despite his inherent differences. He’s flamboyant, somewhat narcissistic, but also competent and diligent. His character arc involves striving to achieve his dreams and making sacrifices for others【51†source】.
Yui from Sword Art Online: Initially introduced as a cheerful girl, Yui is later revealed to be an AI Mental Health Counseling Program. She develops her own intelligence and personality, deeply affecting the main characters, Kirito and Asuna, and playing a significant role in the story【52†source】.
Albedo from Overlord: In the MMORPG isekai anime “Overlord,” Albedo is an AI character with a complex personality, deeply in love with the protagonist, Ainz Ooal Gown. She’s beautiful, calculating, and dangerous, showcasing the depth and complexity that AI characters can possess in anime【53†source】.

These characters demonstrate the diverse ways AI is portrayed in anime, ranging from omnipotent systems to emotionally rich individuals.