You're probably familiar with the depiction of mainframes in films such as Colossus: The Forbin Project (1970). Scurrying white-coated acolytes attend to the needs of the great machine, which is fronted by reels of tape shuffling back and forth, and accompanied by the scream of the dot-matrix printer spewing acres of paper as huge piles of punched cards are consumed and spat out. Meanwhile the computer secretly plots to team up with its Soviet counterpart to take control of the human race.
It followed Stanley Kubrik's 2001: A Space Odyssey (1968), where HAL takes over the space mission to Jupiter, killing all but one of the crew in the process, because it believes they have compromised the mission.
http://www.youtube.com/watch?v=ukeHdiszZmE
It was a trope that refused to die. Consider the Disney film Tron (1982), where the main character hacks into the mainframe with AI - the Master Control Program - which wants to take over the rest of the mainframes.
In books, it didn't take long for mainframes to appear in popular culture. We find the them mainly in science fiction, especially the 'hard' SF of the 1950s and 60s. For example, in Isaac Asimov's short story The Evitable Conflict (1950), mainframes run the world's economy - and of course start to control humans as part of the process. Asimov developed this theme and the mainframes evolved into robots and were tamed by Asimov's much-referenced laws of robotics, which were designed to make humans accept robots.
This depiction speaks to the fear of powerful machines - especially those that few people understood - and is one that was repeated in various forms. You can see parallels with Faust, who sold his soul to the devil. It ended badly. However, the emphasis has shifted, and the machines no longer turn on their creators.
Today, an understanding that "garbage in" usually results in "garbage out" is widespread, a consequence of interaction with personal computers. And, despite ongoing efforts, humans have yet to design a computer - and in popular culture that usually means some form of mainframe - that is truly autonomous from its programming.
Was popular culture ahead or behind the curve? The turning point could perhaps be seen with the appearance of Deep Thought, the computer in The Hitchhiker's Guide to the Galaxy (original BBC radio series: 1978). Though imposing, it presented no threat to humanity - rather, it was perhaps somewhat incompetent. It, and the other computers in HHGTTG, and both Orac and Zen in the BBC's SF series Blake's Seven (1978-81), were flawed – and occasionally even friendly.
Around the same time, IBM's Deep Blue beat the word's greatest chess players, not because it was smarter, but because it had enough processing power to consider the consequences of every available move within a reasonable timeframe. This fact was also widely reported, and probably also helped to shift the perception of the mainframe away from omnipotence.
http://www.youtube.com/watch?v=NJarxpYyoFI
So it's more widely understood not only that computers, including mainframes, are only as good as the information they are fed but that they can be subverted. A case in point is the widely reported case of Gary McKinnon, who is accused of hacking into and damaging 97 United States military and NASA computers. US authorities also said that he left "silly and anti-America messages".
In other words, we have witnessed the cultural progression of the computer, which of course started life as a mainframe, from a frightening machine with untold and little-known capabilities to a tool which, like any other tool, reflects human achievements and frailties and can be used for good or bad.
What are some of your favourite representations of mainframes - good and bad! - in popular culture?