The most pivotal scene in Star Wars Episode II, and the entire series, is when Anakin makes his final decision to turn to the dark side of the Force. I speak of the scene where Mace Windu has Chancellor Palpatine vulnerable and held at the point of his humming purple lightsaber.
Anakin walks in to this environment distressed by his marital problems with Padme, as well as the grandiose thoughts planted in his mind by Palpatine only hours before. Anakin is presented with a choice: stop Mace Windu and join Palpatine as his new dark apprentice (which we all know is what happens) OR agree with Mace Windu and allow the Chancellor to die.
I submit that, if Anakin chose the latter, the fate of the entire galaxy would have shifted tremendously and a different story would have been told in Episodes IV-VI. Allow me to paint you a picture to ponder over...
Mace Windu slays the weakened Chancellor Palpatine (perhaps with Anakin's help if Palpatine was merely playing opossum). Anakin would be upset, but would now have the comforting, although blunt, words of Mace Windu to console him. Mace would explain the consequences of their actions, and the even more dire consequences had they allowed him to live. Anakin has already made morally gray decisions throughout the Clone Wars, and I believe he would eventually come to understand he did what was right.
Then what would happen...?
Order 66 would never had happened. That's right, all Clones have the order to obey the Chancellor no matter what, but with him eliminated their obedience would fall back to their Jedi Generals. The Clone Army would continue its war to preserve the Republic and the Jedi Temple would still stand without the casualties caused by Anakin and his Clone brigade's raid. The future of the Order, and the masters of the Order, would be alive and well.
But, what would happen to the villainous Confederacy of Independent Systems and their droid armies?
Obi wan Kenobi had eavesdropped on General Grievous' meeting with the CIS head-honchos on Utapau. With the same outcome as the movie, Kenobi would have stood victorious alongside his Clone troops in the battle that followed his arrival. However, without Order 66, Kenobi would have reported back to the Jedi Council with the information he gathered from the overheard meeting. This would have prompted the Council to dispatch (most likely) Kenobi and (maybe) Anakin to Mustafar and arrest the leaders of the CIS. As in the film, Mustafar was barely defended, having very little droid troops located there. Kenobi and Anakin could have easily taken the outpost and apprehended the traitors to the Republic.
What next, you ask?
The Senate would reconvene and, most likely, reestablish a near-galaxy-wide Republic once more. Of course, they would be upset at the death of Chancellor Palpatine by the hand of a Jedi...until they heard testimony from Anakin, publicly known to be the closest Jedi to the Chancellor, discrediting the Chancellor and explaining Palpatine's evil plans. A new Chancellor would have been elected, and I'm sure there would be a few systems that stayed outside of the Republic for whatever reason, but the Republic would still stand as a shining tribute to democracy. The Jedi Order would still stand in a recoverable stance and look to the training of its future generations.
But, what would be told in the original trilogy-era, a decade or two after this?
Not only would Anakin and Obi wan become masters of the Jedi Order, but I believe they would push to change the Order for the better. Anakin and his marital status would come quickly into question in the face of the Order, but I think with his critical insight into the "faults" of the Order, and Obi wan's backing, the Order would be altered slightly enough to preserve its intent as well as fend of any more desires to leave in the name of passion. Anakin could grow old with Padme at his side, and he could train his son at the academy to become another legendary Skywalker.
Finally, though, who would be the "bad guys" in the original trilogy if not the Empire?
Without the Empire, I believe the Yuuzhong Vong would have invaded much earlier (that is, if they are still accepted as canon now that J.J. Abrams has discredited all Expanded Universe story lines). This would have accelerated not only their decimation over the galaxy, but also the emergence of Darth Krayt. The Jedi Order, and the Clone Army, would have spent several years fending off the Yuuzhong Vong. Then, as Darth Krayt rose to power, Luke Skywalker along with his father and Obi wan, if they were still both alive, would have focused on the newest Sith threat in the galaxy. I believe with the Jedi Order at such great heights, two Skywalkers leading the charge, and the sage-like Obi wan, the Order would have been successful in stamping out the dark powers that would have invaded their galaxy.
Thank you for reading! Please let me know what you guys think! I'm a devoted Star Wars fan, and enjoyed writing every word of this!