Skynet's primary pop culture forebear is the treacherous HAL 9000 in Stanley Kubrick's 2001: A Space Odyssey, but science fiction writer Isaac Asimov is perhaps best known for exploring the danger to humans that an AI may pose. In the video game universe, Skynet (and its Terminator creations) shares similarities to the Geth in Mass Effect, the AI in The Matrix, and the Separatist battle droids in Star Wars.
While the T-800 and T-1000 machines are generally seen as the "villains" of the Terminator franchise, it was Skynet that initiated the nuclear war and designed Terminators to eliminate the few surviving humans. In the original timeline of The Terminator (1984) and Terminator 2: Judgment Day (1991), Skynet's creators attempted to pull the plug after the system became "self aware." Skynet responded to this threat to its survival by launching America's nuclear arsenal against targets in Russia, precipitating Russia to launch its own weapons (a Cold War scenario known as "mutually-assured destruction," or M.A.D.). The nuclear war killed billions and forced humanity underground.
Despite seemingly insurmountable odds, the remnants of human society banded together to resist Skynet's final solution. Led by a man named John Connor, the human resistance eventually smashed Skynet's defense grid and defeated the genocidal AI. However, just prior to its destruction, Skynet was able to send a T-800 Terminator back through time. It's mission was to kill John Connor's mother, Sarah, thereby preventing John from being born and leading humanity to victory. The Terminator failed in its mission.
In the second film, Sarah discovers that Skynet sent another Terminator (the T-1000) to target John when he was a small boy. Rather than simply run from this machine as she had done in the past, Sarah took a page from Skynet's playbook: she attempted to change the course of events. With the help of her son, a remorseful computer expert, and a reprogrammed T-800 sent back by the resistance to protect John, Sarah blows up the Cyberdine Systems lab where Skynet will eventually be created.