Since the theme of this thread seems to be choosing the particular mechanics of fictional iterations of timetravel we like best and declaring them THE TRUTH, I choose this guy's:
While fairly complicated, this take makes the most sense to me and its also pretty cool, which is all the better. He only covers the first two films, but following his logic, both T3 and TS can be included. It also has implicatins for TSCC and how the shifting timelines were hinted at there. Hopefully he'll get to them all at some point. He dissects a whole bunch of other timetravel movies on the site, the latest being Deja Vu
Oh, and I voted yes, there was an original timeline where someone related to Sarah Connor was enough of a pain in something resembling Skynet's ass that it whipped out timetravel as a not too completely insane solution to the problem. Whackiness ensued.