well, my Favorite AI that i didn't make is the Red Dwarf's AI, Holly, a AI with the IQ of 6000 who is left alone for three million years and goes completely senile and IQ lowers to 6.
and the AI that i came up with: an AI who, as soon as they uploaded the sci-fi section of the world, he decided to change his name from Harry to Hal and the name os the base he lives on to D.W.H. Airsoft (D.W.H. stand for Disaster Waiting to Happen, and the base is an Orbital facility) he is insanely smart but is hampered by a non-serious attitude and tend to dislike being ordered around (he DOES have Asimov's laws programed into him, or atleast something similar) so he tends to does what he was ordered to do, but in a roundabout way, and sometimes givng the person something completely other than what they wanted to teach them not ot give him orders, but instead to ask him to do something...