First films to feature the internet/world wide web.

[thenoise]

July 1966 - Features a computer that can think for itself that is soon to be connected to other computers around the world via telephone lines.  Eventually decides that it is cleverer than humans so it should rule over them.

Is supposedly really intelligent, but it refers to the doctor as 'Doctor Who' on one occasion, and repeatedly describes him as having a 'human brain'.

[BlodwynPig]

Quartermass

[NoSleep]

That's spelt "Cratermass".