According to the 1991 movie Terminator 2: Judgement Day, August 29th is the day Skynet becomes self-aware.
The Terminator: The Skynet Funding Bill is passed. The system goes on-line August 4th, 1997. Human decisions are removed from strategic defense. Skynet begins to learn at a geometric rate. It becomes self-aware at 2:14 a.m. Eastern time, August 29th. In a panic, they try to pull the plug.
Sarah Connor: Skynet fights back.