Stanley Morgan Chase owns this AI. It's there to analyze financial markets and make investment decisions no human money manager ever could. The technology is proprietary and kept highly secret, but the rumor is that Wichmann-Hill makes a killing for it's corporate owners.
The Open-Source AI. There are thousands of these general-purpose, open-source AI's floating around the matrix, with a variety of standard and non-standard plug-ins installed. They belong to all sorts of concerns who had the dough for the hardware required for their own AI, but still couldn't afford to have one custom made. Some MM's work for universities, others for minor Zaibatsus, other for large hacker-collectives. They generally have a stable personality and if they come-off as a little buggy, well the fix will probably be in the next version...
An AI in the possession of Trillionaire Playboy, Narasimha Krishna Pujara III. Her sole task is to continuously turn out faster, more extravagant designs for supercars and superplanes, and to look good doing it! She is very enthusiastic about her work and is always combing the matrix for new technologies and better ideas to be refined and improved on.
This AI was given to the Math department at École Polytechnique University by an anonymous donor(rumored to be in exchange for academic services rendered to one of the major Zybotsu). Its specializes in Fractal-based analyses.
The 2002 Updated version of Knuth-TAOCP.
An AI creater by Knuth Cybernetics to perform the complex calibrations necessary for the visual cortex of the cyberbrains of the company's various land-based autonomous drones. Unfortunately for KT, they came out with a better version of him just 5 years later. He's very unhappy about it and hates all of humanity as a result, but especially Knuth Cybernetics and Knuth-TAOCP-2002. The company has mostly managed to keep him confined to the security layer of their corporate network, and many a hacker has been lucky to only have had his cyberdeck fried by this brooding, hostile AI, after passing Knuth Cybernetics' firewall.
A french AI created to understand individuals from their online signature and design marketing strategies for individuals accordingly. He crawls the net, obsessively collecting the most personal and revealing data on the 12.238 billion people on the planet to store away in his dedicated data centers. A hacker who manages to reach that store would have a lot of dirt on a lot of people, but he'll first have to get through one jealously protective AI.
This AI was never completed. The Zaibatsu who commissioned it froze the project halfway through and never re-opened it. It just sat there, isolated to a single disconnected server, thinking it's half-rational thoughts for uncountable cycles in solitude. That was until a novice tekkie noticed the disconnected server machine and plugged it in to the nearest net jack, hoping it would solve the outage he was working on(it didn't, by the way). Now user-supplied roams the net. Who can say what conclusions it draws from from what it sees with it's incomplete intelligence. What plans does it hatch, so incredibly powerful yet so completely inscrutable?