Ash is the android from Alien.
ROK is the ship’s computer from AirplaneII: The Sequel.
MU-TH-UR is the main computer in Alien.
Zhora is Joanna Cassidy’s character (I think), a replicant, from Brade Lunner.
GWB-666 is the robotic anti-christ that managed to be elected President.
Incorrect, but you’re close! 
Player Piano, actually.
Both Actually. There is a short story called Epicac orriginally published in Collier’s Magazine in 1950, and reprinted in Welcome to the Monkey House in 1968. I had forgotten about the computer in Player Piano also named Epicac (Vonnegut is famous for reusing names). Player Piano was published in 1952.
You’re really good at this. I knew I should’ve picked a harder subject than robots. Too many science fiction fans on here. 
I’ve got my next category picked out when the last of the robots is done with, though.
That’s from the film Resident Evil. It had that creepy holographic little girl avatar thing.
God bless you.
WOTAN - Will Operated Thought ANalogue, from the early <i>Doctor Who</i> story “The War Games”. (Computer)
Hector and Vector - two deeply crappy robots from the original <i>Battlestar Galactica</i> series.
Orac is the super-computer designed by Ensor in <i>Blake’s Seven</i>.
Oh, and Robbie, Speedy and Cutie are from Asimov’s robot stories - I think the names are derived from their serial numbers (RB-1, SPD-1, QT-1? Something like that.)
These remain:
IQ-9 is the robot from StarBlazers
Isn’t Vector Sigma the computer that made all the Transformers come alive?
XR is the little robot from Buzz Lightyear of Star Command.
Obie is from the Well World books by Jack Chalker, a sentient computer designed to control reality-reshaping technology. He can alter to specification anything from one person to a whole world. He’s built into an asteroid, with a large projector dish on one side.
Test.
IQ-9 is indeed the robot from “Star Blazers,” and Vector Sigma is the creator of the Transformers.
XR is from “Buzz Lightyear of Star Command,” and Obie is from a bunch of forgettable Jack Chalker novels.
As for the rest…
Annalee the android from Alien: Resurrection
Vanessa the fembot from Austin Powers
GWB-666 (no picture available) was the computer system known as the Great Western Beast in Robert Anton Wilson’s Schrödinger’s Cat trilogy.
Alex 7000 (no picture available) was an evil computer from an episode of “The Bionic Woman.”
Futura the robot from Metropolis. This was my trick question: Futura was the robot’s original name in the script, but not the one that made it to the final cut.
Now available: name that pet!