I'm a fan of the robots in Metropolis, Forbidden Planet, The Iron Giant, The Day the Earth Stood Still, Silent Running, Star Wars, Pacific Rim, West World, The Incredibles, THX 1138, The Matrix, Sky Captain and the World of Tomorrow, and even Robots, among many other movies. And Isaac Asimov's tales of robots, robotics, and roboticists (but emphatically not their movie derivations) are my favorite stories.
But what prompted me to start drawing android robots was The Questor Tapes, an obscure 1974 TV movie. This was a Gene Roddenbury series pilot, though creative differences killed the series before it started. Though I've since forgotten most of it (I only saw it that one time), I still remember the scene where the android, late at night and unknown to its human engineers, refines its own appearance from blank mannequin to realistic human.
After that, I was sidetracked for a few years by college and other forms of experimentation, but eventually I resumed drawing bits and pieces of android robots. The human shoulder in particular presented a vexing (but fascinating) engineering challenge.