If you define sentience to mean "the ability to feel or perceive," then a wide array of animals are sentient. Look at any pet cat or dog to see a display of feelings like fear, excitement, or curiosity.
If you take a more narrow definition of "being aware of one's own existence," I imagine you would still find a number of animals who fit into the category.
An African Grey Parrot, while learning colors, asked what color his feathers were. https://en.wikipedia.org/wiki/Alex_(parrot); I would imagine there is a strong likelihood that you would probably see similar levels of self-awareness from other animals if we had a better way of testing for it.
After all, there's nothing so special about Humans and Parrots in particular, is there?