Another idea that was siting in my head...
Imagine one of the versions of Skynet destroying the Human Resistance. Without the humans to fight, Skynet (now referring to itself as Skynet Prime) seeks to increase it's technological base exponentially. So it discovers dimensional travel technology, and begins to search the multiverse for other mechanical life. Three parallel earths later it discovers another Skynet. Logically, Skynet Prime's superior technological abilities would make an alliance between the two Skynets as foregone conclusion.
The war that broke out was much greater than Skynet Prime had anticipated. And it soon involved the Skynets from other timelines.
Skynet Prime has won many initial battles with the alternate Skynet timelines. A stalemate soon developed that was only broken when the final breakthrough was found. A stray probe found the coordinates for Terminator Prime, the original timeline that all other timelines branched out from. Now each Skynet plots to reach Terminator Prime to either rule the universe or end the mechanical madness once and for all.
Ideas for alternate Skynets include:
*A world where the technological basis of the Terminators was reverse enginered by the remenants of alien invasions. From the Dalek and the Cyberman invasions of the 70s and 80s.
* On a parrallel world where the Reich overran the free world fifty years before, the Nazi's rule a terrified world. As the fires burn over the last city in the United States, a signal goes to a secret bunker deep within a secret location. A red light begins to burn in the eyes of an army of skeletal robots, and soon the Nazis will know fear...
* A world where Skynet was infected with the ramblings of a madman. The book the madman was carrying was Necromicon Ex Mortis, the Book of the Dead.
* Skynet is a giant babbage machine built after the first invasion by the Martians. It soon goes rogue, and man must fight the clockwork army that was meant to protect its creators.
* Skynet was the first bio-computer created that could tap into the limitless storage capacity of the DNA Helix. The Terminators created by this Skynet are amongst the most terrifying things man can see.
One could play this as a superheroic dimensional travel game as supers try to keep the Skynet war from spilling out into the multiverse. Even more fun could be is for the players to each play a Skynet. This is perfect for miniature or board game type play. Each Skynet would have a set amount of Hunter Killers, Infiltrator Terminators, aircraft, etc. A system would be provided to individualise each faction.
Robocop vs Terminator: A great miniseries, the main source of this idea.
GURPS Reign of Steel: Great reference for two reasons. First, it shows one way how AIs would wage war, both hot and cold, against each other. Second, it's probably the closest you'll get to a Terminator roleplaying game.
Terminator: The main wikipedia entry on the Terminator franchise.
Terminator: The Sarah Connor Chronicles: The late Fox TV series, which had hints of alternate timelines and different versions of Terminators working against each other.