R2-D2 saved the Queen's starship in Episode 1. Without Artoo, the ship would have been destroyed, and the Jedi killed, as well as the queen. Nute Gunray is successfully prosecuted for invading Naboo and killing the queen. Qui-Gon and Obi-wan would never have stopped on Tatooine to find Anakin, and so Anakin would never have become a Jedi, nor would he have become a Sith. A new leader of Naboo would have been elected, and as Jar-Jar had been killed as well, he wouldn't have called for emergency powers for the Chancellor, even if the Trade Federation had remained intact after that fiasco. In short, if Artoo had never existed, the Empire would never have been formed.

"I don't know what all the trouble is about, but I'm sure it must be your fault."