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Terminator: Arnold Schwarzenegger can't act but has bodybuilder muscles so he gets to play murder robot from the future in 80s sci-fi which coined the term "tech noir" for being the first major movie that didn't believe technology will save us, but instead is a threat.
T2 Judgment Day: Brings in most advanced 3D graphical effects of the time in the form of the liquid metal Terminator and expands the idea of AI being a threat, had a huge impact on the general view on AI as bad.
T3 Rise of the Machines: Odd story progression where the adversary is an Anti-Terminator Terminator with weapons built into the arm, made for destroying Arnold, then ends with nuclear war and humanity destroyed.
Anything else: not canon and just made to make more money on it.