I've got ten.
Based on the God awful Terminator: Genysis trailer, I've finally compiled the OFFICIAL Terminator timeline/timelines. I know there are things floating around on the internet showing a possibility of split timelines, maybe three or four, but again... I got TEN. If anyone wants to make a graphic, by all means, please do!
A few things before we begin:
I will be referring to Chaos Theory a shitload:
"Chaos theory is a field of study in mathematics, with applications in several disciplines including meteorology, sociology, physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions -- a response popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction difficult in general.  This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved.  In other words, the deterministic nature of these systems does not make them predictable.  This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as follows:  Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Chaotic behavior can be observed in many natural systems, such as weather and climate.  This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Pointcare maps." - Wikipedia
Henceforth, I will be using the words "timeline" AND "universe" interchangeably. The idea is each "alternate universe" created by Kyle Reese in the first Terminator movie is a "split timeline" from the original "prime one." As if this wasn't obvious, MAJOR SPOILERS FOR THE ENTIRE TERMINATOR FRANCHISE. *note* I'm not counting the Expanded Universe (i.e. comics, games, books, toy lines, or TV show) as "canon" unless someone can provide an official reason I should.
And here... we... go.
TIMELINE 1: TIMELINE ALPHA THE ORIGINAL 1984-2029
Sarah Connor marries/has (a) child(ren) with an unknown man circa 1984-1991. An unknown company/inventor/researcher creates Skynet, a self aware AI (Artificial Intelligence) for the purpose of controlling unmanned drones and bombers. The chief scientist behind this is also not known.
Skynet, built as a Global Defense System, is put in control of NORAD and becomes self aware circa 2:00 am, August 29th 1997. It launches all of our nuclear missiles at Russia, knowing the Russian counter attack would likely end the civilized world. The world "ends" August 29th, 1997, an event which comes to be known as "Judgment Day." Sarah Connor likely never even hears the word "Skynet" or survives this event. A small percentage of humanity survives and begins a war with the machines, which are learning and evolving at an advanced rate.
John Connor, Sarah's surviving son, manages to lead the human resistance against the machines circa 2027-2029 and capture a time machine. The machines learn the identity of Connor and perceive him as their greatest threat. Realizing they can rewrite history/steal a victor, send a Terminator back in time to kill Sarah Connor. Kyle Reese, becoming infatuated with her picture/stories about her, elects to go back in time to protect her.
TIMELINE 2: THE EVENTS OF TERMINATOR/THE EVENTS OF THE ORIGINAL TIMELINE OF T-2
For a bit of a visual aid, we will give you the players in the following timeline (Timeline 1 doesn't get one, seeing as it happens prior to the events of the first Terminator movie.)