And to try and get back on topic here...
Someone already mentioned dolphins being self aware. There are several other animals that are also self aware (my parrot being one),,, but octopuses are extraordinarily self aware. Their ability to camouflage their body to mimic their surroundings or even mimic other animals is really unmatched in the animal kingdom.
They are watching us,,, AND,,, they make themselves invisible while they do. They can't be trusted!
There is something that research on the treatment of depression and anxiety have found (specifically a type of psychotherapy called ACT). It's odd that it sort of grew out of this body of reasearch. Anyway, what the research was about how human beings thinking influences their mood. Well as the research came out, the investigators starting coming up with an idea called "metacognition" and a theory called "relational frame theory". Since this, more and more evidence is pointing to this being something very real and something that has made our species so ridiculously good at learning and understanding, and by extension, thriving.
Relational frame theory is very, very complicated and I really only understand a little bit of it, but it basically discusses how humans can learn so much more efficiently than any other species. Basically because we have such complicated language we can actually describe scenarios that we can learn and then predict something from. This is how it grew out of depression and anxiety research. For instance, I don't like flying in planes. I always avoided it. But, I never flew on a plane, so why should I be so anxious? It's because I could imagine a scenario where I'm in a plane and the plane goes down, and I die. I never actually experienced this so I should not be anxious about it. This is extremely useful.
In the evolution of humans we could tell others that if you're looking over the Safari grass lands and you see the grass move in a specific spot to run, it might be a lion coming to eat you. We can understand this scenario and can envision it before it happens. So when we do encounter a possible lion we run. This allowed us to survive. But even more it allowed us to pass on very, very complicated ideas to other people from how to drive a car to the theory of relativity. In other words we can think about thoughts and ideas. There is only one two other animals that have been shown to do this: a bonobo (type of ape) and a sea lion. I used the word "a", just two organisms outside of humans (and yes dolphins were tested).
To make a long story short, if humans get wiped out and another species comes to dominate like we do, I'd put my money that it comes out of the apes, perhaps a bonobo.