Half of me is offended by what the movie I, Robot does to Isaac Asimov's universe. The heart is in the right place -- to a certain extent -- but it messes up some characters and it throws a huge monkey wrench into the pre-Empire timeline. But, I did get a kick out of the references to his stories. I can think of three off the top of my head. (Warning: Spoilers ahead.)
- Near the beginning of the movie, Dr. Calvin and Detective Spooner are trying to find the "malfunctioning NS-5" in a warehouse of 1000 other non-malfunctioning but otherwise identical NS-5's. In the Little Lost Robot, Calvin is trying to sort a robot with a modified First Law from a group of otherwise identical robots. Her proposal in the movie - interviewing each robot and correlating their responses - is what she first tries in the story. Even more amazing, the model number for the robots in the short story is NS-2.
- Sonny's dreaming, and the dream itself, are taken almost verbatim from the story Robot Dreams.
- Viki's interpretation of the three Laws (and thus the very climax of the movie) is very similar to R. Daneel Olivaw's development of a Zeroth Law in the Empire series.
Add to that the very prominent position of Dr. Susan Calvin, Alfred Lanning, and Lawrence Robertson in the movie (not to mention the Three Laws and the title itself), and you have a movie that borrowed pretty heavily from Asimov's work.
Update: Damnit, IMDB's trivia page for I, Robot listed all three of my references.