I have to go with the chameleon.
Since I was little, I loved dinosaurs, but since they had to go and become extinct 65 million years ago before my existence, I generated an affinity to reptiles rather quickly. Everything from snakes to tortoises, I was just enamored with the verity and complexity of these creatures to the point that I considered owning one (though didn't because I feared at the time that one of my relatives might kill and eat them; a fear that is still very prevalent to this day).
Instead, I came to admire the chameleon and all that it is capable of: it can change colors to better suit its surroundings, they have long tongues that allow them to reach for things out of their grasp, they hold firm and never let go, their eyes allow them to be aware of everything at all times, and they go slow, soaking in everything around them.
It's easily the animal that I identify with the most.