I know that you must suspend your disbelief during any type of time travel story, but the Terminator movies make it really hard by throwing paradoxes right in your face. I abhor a paradox, and therefore have tried to explain time travel in the Terminator movies in this way:
1. At some point Sarah Conner meets someone else and has a baby, John Conner. The father is not Kyle Reese. This John Conner still becomes the leader of the resistance and as he is about to deliver the final blow to Skynet in 2029, discovers the plan to send a T-800 back in time to kill his mother, he sends Kyle Reese back to protect her.
2. Reese going back changes the timeline in 2 ways: first, he is now the father of John Conner, and, second, Cyberdyne now has the hand from the original T-800 to speed up its work.
3. Now there is a different John Conner who is trained by his mother to lead the resistance, but, as Terminator technology has advanced significantly, Skynet has built a T-1000 by the time John Conner is about to win, again in 2029, and sends it back in time to kill John as a teenager. John sends a reprogrammed T-800 back to protect himself. Miles Dyson helps them destroy his work, this slows down Judgement Day, but does not stop it, as Cyberdyne would have some info backed up offsite and the Airforce takes over. But this does alter the timeline enough that John does not win in 2029 but later in 2032.
4. After John has defeated the robots and he is killed by a T-800, his wife finds out that, though defeated, Skynet tries one last effort by sending the T-X back in time to kill as many of the Resistance leaders as possible. The T-X fails because Conner's wife reprograms the T-800 that kills John and send it back to protect John and the leaders in the past. The T-X is defeated, but Judgement Day cannot be averted as Skynet is satellite software and cannot be shut down.
5. Terminator Salvation takes place in 2018 before John Conner (son of Sarah and Kyle) manages to get the upper hand on the robots; however, we must assume that John Conner is a significant enough thorn is the side of the robots that they feel the need to kill him now. In another 9 years John will be about to win, send a Kyle back, send the T-800 back and then 3 years later he will win, die, and his wife will send the T-800 back.
6. The Terminator timeline ends with the machines defeated but John Conner as a martyr.
So the events would look something like this:
1984 - John Conner born
1991 - Cyberdyne building blown up, Air Force takes over research
2004 - Judgement day (pushed back from 1997)
2018 - events of Terminator Salvation
2029 - Kyle Reese sent back, 2 T-800s and T-1000 sent back
2032 - Machines defeated, T-800 sent back after killing John Conner, T-X sent back
It is not a perfect explanation but it is the best one I could come up with.
