This article is from the The Terminator FAQ, by Karsten A. Loepelmann firstname.lastname@example.org with numerous contributions by others.
According to the classical, single timeline/universe view, it is impossible --
unless Cyberdyne Systems develops Skynet technology *independently* of any
help from the future.
Assuming the existence of a multiverse of timelines, this situation can also
be explained. In the universe in which we see the Terminator technology
destroyed, Skynet will never exist. However, there must exist at least *one*
timeline/universe in which Skynet technology is developed. This may occur
due to: a) Cyberdyne independently creating the technology, or b) Terminator
remains originating from yet *another* timeline are left behind. Thus, the
movies must chronicle *two* different universes: one with the hellish future
dominated by Skynet, the other is the one saved by Sarah and John.