Have any movies been produced based on Isaac Asimov's Foundation series? If not, why not?
As explained on the Wikipedia article, there has not been a movie. The reasons why a movie has not been made for a book or series generally (including this case) come down to one thing: money -- or more specifically, a lack thereof. The Foundation series appears to be in what is often called development hell, characterized by repeated (failed or stalled) attempts at making a movie since 1998.
Right now, the rights for a Foundation series of films have been given to Roland Emmerich and he plans to get to development on them after his next movie. It seems he is planning a CGI/3D opus (ala Avatar) and will likely over-convolute the story with action and special effects =/
(This is not really a movie and it is not explicitly referencing the Foundation series from Asimov, but it is directly inspired from it and heavily borrows its key concepts, so it could be something of interest)
There is an episode from Star Trek: Deep Space Nine, named Statistical Probabilities (Season 6, Episode 9) that is inspired by the concept of psychohistory. In the episode, a group of genetically augmented persons is so intellectually advanced that is able to predict and calculate the outcome of the Dominion War.
Quote from the Deep Space Nine Companion, as reported by Memory Alpha (bold text by me):
The story line was based on Isaac Asimov's classic Foundation Trilogy. Asimov based his work on issues raised in Edward Gibbon's The History of the Decline and Fall of the Roman Empire, and the basic plot involves a scientist (Hari Seldon) who develops a branch of mathematics known as psychohistory which he uses to calculate that galactic civilization is doomed to fall, leading to 30,000 years of darkness and barbarism. Seldon, terrified at this prospect, takes action to attempt to minimize the oncoming "dark ages" to only 1,000 years, but his plan fails to foresee that the actions of a single individual could render his predictions invalid. Psychohistory is based upon mass action, and it can only predict the future when dealing with large groups, predicting trends in large masses of people, which is why Seldon is unable to take into account the actions of individuals – when it gets down to individual people, the variables become so vast as to be impossible to calculate, so the predictions become unstable. In the novels, a character called The Mule, who has psychic abilities, becomes intimately involved in events, and directly influences their outcome, something which Seldon's psychohistory could never have predicted. This is exactly what happens in the episode: the savants make large scale predictions based upon mass action, but they fail to take into account the actions of one single individual, who comes to directly affect everything they have predicted.
Emmerich has been saying he is going to make a movie since 2009, the movie is slated for 2013 (according to IMDB) and so for not a single actor/set/premise/detail has been disclosed. Emmerich is quite frankly a terrible director who lacks the ability in making anything good. I hope it stays in movie hell until some competent hands are capable of dealing with it.
MORE RECENT NEWS
Deadline reports that the project from Skydance Television is “in development for straight-to-series consideration,” with David S. Goyer and Josh Friedman attached as showrunners. Goyer is best-known for comic book adaptations like Blade, Man of Steel and Batman v. Superman: Dawn of Justice, while Friedman was the creator of Terminator: The Sarah Connor Chronicles.
According to TheWrap, Jonathan Nolan is writing a TV series based on the Foundation Cycle to be produced by HBO. Anyway, that article is rather old (November 2014), and as far as I know, there have been no other concrete news about this project.
An article from iDigitalTimes (July 2016) doesn't really add anything, besides assuming that there is no any real reason to believe that this project was canceled (but, I can add that we don't even have any proof that it is going further).
A discussion on Reddit also contain nothing more than a bit of speculation.
The only tangible outcome of this rumor is a fan-made opening titles video. It is extremely amazing, but is just a fan product, unfortunately id doesn't really have a meaningful significance about the status of the project.