In a way nuGalactica has gotten there first and done it better but Obi-Wan sort of preempts the idea by saying something to the effect of "If droids could think none of us would be here". Yet we see Artoo and Threepio go through much the same motions as the human and alien characters.
You say we don't see the droids deep in thought but we see them (or at least seem to see them) as contemplative as any of the other characters.
The sequence that George screwed up by adding his appearing/disappearing rock shows Artoo display or at least appear to display a range of emotional responses.
Fear, concern for Luke and even recognition of Obi-Wan and the completion of his mission.
He later shows concern for Threepio.
He has much more of an acting range than even Ewan McGregor in the PT.
So essentially the peoples of the Star Wars universe (surrounded by droids) are living on the edge of a potential catastrophe.
It just needs a spark, provided by a good villain.