Not to be glib, but our brain is the only organ, in all living beings on earth,as far as we know, that can wonder about itself and write at lengths about itself.
Obviously dogs won't write about their brains being sentient, but how do you know that they don't think about themselves?
Humans were sentient long before they knew how to write, or which part of the body is responsible for their thoughts. What makes us think we're so special?
I am quite sure dogs can predict future behaviour of simple systems and act on these systems to achieve their goals. Problem solving in dogs is widely documented and I think it suffices to assume at least some sentience.
You're so right, and it seems one sees this error constantly in discussions like this. Human beings like us have been around for 200,000 years, and only within the last 10,000 have even some of us written anything down. Yet we assume that civilization, with farming and government and writing, is somehow the default for this species.
http://en.wikipedia.org/wiki/Mirror_test - there is a discussion about dogs specifically, noting that vision is not their primary sense, so the mirror test may have less value.
Here's also a video on her, as well as Koko, a gorilla that was also taught ASL[2]
[1]http://en.wikipedia.org/wiki/Washoe_(chimpanzee) [2]http://www.youtube.com/watch?v=3V_rAY0g9DM