For the purposes of this timeline I am using information solely from the movies The Terminator, Terminator 2: Judgment Day and Terminator 3: Rise Of The Machines. Information from other sources is ignored, since the production of Terminator 4 is likely to do the same.
T3 explicitly acknowledges that there are multiple timelines in the Terminator universe. I have managed to pare this down to a conservative one timeline per movie, plus one initial timeline.
Terminator: The Sarah Connor Chronicles is said to provide an alternate sequel to T2 and therefore occurs in a separate timeline from T3. I'm waiting for more information before incorporating it below.
This timeline is not shown in any movie.
Sarah Connor conceives John Connor by an unknown father. [John Connor may not be a genetically identical individual in each timeline; he is, after all, played by a different actor in every appearance.]
Skynet is researched and built, from scratch.
Skynet becomes self-aware.
Judgment Day occurs.
2029: John Connor leads the resistance against Skynet.
In a last-ditch attempt to avert its own destruction, Skynet sends a T-800 back in time to assassinate Sarah Connor before John Connor is born. John Connor sends Kyle Reese back in time after the T-800. These two temporal incursions create Timeline B. The assassination attempt fails.
Skynet is defeated?
A T-800 arrives from the future to kill Sarah Connor.
Kyle Reese arrives from the future to protect Sarah Connor.
Sarah Connor conceives John Connor with Kyle Reese.
The T-800 is destroyed in a hydraulic press and Kyle Reese is killed.
Skynet is researched and built from the remnants of the T-800.
August 4, 1997: Skynet becomes self-aware.
August 29, 1997: Judgment Day occurs.
2029: John Connor leads the resistance against Skynet.
In a last-ditch attempt to avert its own destruction, Skynet sends a T-800 back in time to assassinate Sarah Connor before John Connor is born. John Connor sends Kyle Reese back in time after the T-800. These two temporal incursions do not create a new timeline but reinforce a causal loop in this timeline. The assassination attempt fails.
Skynet sends a T-1000 back in time to assassinate John Connor as a child. John Connor sends a reprogrammed T-800 back in time after the T-1000. These two temporal incursions create Timeline C. The second assassination attempt fails.
Skynet is defeated?
A T-800 arrives from the future to kill Sarah Connor.
Kyle Reese arrives from the future to protect Sarah Connor.
Sarah Connor conceives John Connor with Kyle Reese.
The T-800 is destroyed in a hydraulic press and Kyle Reese is killed.
Research begins on the remnants of the T-800.
A T-1000 arrives from the future to kill John Connor.
A reprogrammed T-800 arrives from the future to protect John Connor.
Both Terminators and the remnants from the original T-800 are destroyed. This does not avert Judgment Day, it is merely postponed.
1997: Sarah Connor dies of leukemia.
Skynet is built from scratch.
Skynet becomes self-aware.
July 24, 2004: Judgment Day occurs.
2029: John Connor leads the resistance against Skynet.
In a last-ditch attempt to avert its own destruction, Skynet sends a T-800 back in time to assassinate Sarah Connor before John Connor is born. John Connor sends Kyle Reese back in time after the T-800. These two temporal incursions do not create a new timeline but reinforce a causal loop in this timeline. The assassination attempt fails.
Skynet sends a T-1000 back in time to assassinate John Connor as a child. John Connor sends a reprogrammed T-800 back in time after the T-1000. These two temporal incursions do not create a new timeline but reinforce a causal loop in this timeline. The second assassination attempt fails.
Skynet sends a T-X back in time to assassinate John Connor and his future generals as young adults. Katherine Brewster reprograms the T-850 and sends it back in time to protect him. These two temporal incursions create Timeline D. The third assassination attempt fails.
Skynet is defeated?
A T-800 arrives from the future to kill Sarah Connor.
Kyle Reese arrives from the future to protect Sarah Connor.
Sarah Connor conceives John Connor with Kyle Reese.
The T-800 is destroyed in a hydraulic press and Kyle Reese is killed.
Research begins on the remnants of the T-800.
A T-1000 arrives from the future to kill John Connor.
A reprogrammed T-800 arrives from the future to protect John Connor.
Both Terminators and the remnants from the original T-800 are destroyed. This does not avert Judgment Day, it is merely postponed.
1997: Sarah Connor dies of leukemia.
A T-X arrives from the future to kill John Connor and his generals.
A reprogrammed T-850 arrives from the future to protect John Connor.
Skynet becomes self-aware.
Both Terminators are destroyed.
Judgment Day occurs.
2029: John Connor leads the resistance against Skynet.
In a last-ditch attempt to avert its own destruction, Skynet sends a T-800 back in time to assassinate Sarah Connor before John Connor is born. John Connor sends Kyle Reese back in time after the T-800. These two temporal incursions do not create a new timeline but reinforce a causal loop in this timeline. The assassination attempt fails.
Skynet sends a T-1000 back in time to assassinate John Connor as a child. John Connor sends a reprogrammed T-800 back in time after the T-1000. These two temporal incursions do not create a new timeline but reinforce a causal loop in this timeline. The second assassination attempt fails.
Skynet sends a T-X back in time to assassinate John Connor and his future generals as young adults. Katherine Brewster reprograms the T-850 and sends it back in time to protect him. These two temporal incursions do not create a new timeline but reinforce a causal loop in this timeline. The third assassination attempt fails.
Skynet is defeated?