|"My lord, there are so many uncharted
settlements," says Ozzel. TESB opens with the Empire
busily searching the galaxy with "thousands" of probe
droids searching for the Rebels. Remarkably, Darth Vader chooses to
divert probes to the Hoth system - a system dubbed low priority by the
admiralty, because it is uninhabited.
From this, we know that there are at least thousands of systems on the Empire's charts that are quite uninhabited.
Later on, we also see Cloud City (Bespin). This is a cloud-mining operation and settlement that the Empire had no control over. Lando's discussion with Vader does not suggest that this is an unusual state of affairs; thus, while the Empire has no rivals, it does not actually hold all of civilization in its grasp. There are not only Rebels, but a wide assortment of independents floating around.
on the Imperial Probe Droid.