Where are the whites of the eyes in other animals?

In most primates, the outer fibrous covering of the eyeball, or sclera, is pigmented and appears as a uniform or dark brown color. Brown coloration of the sclera provides little contrast with adjacent tissues, including the facial skin surrounding the eyeball and the pupils (brown pupils are the norm for all primates, save for humans and some lemurs), making it difficult to detect the position of the iris and thus the direction of gaze in nonhuman primates. Humans have a transparent conjunctiva and lack pigmentation in the sclera, giving us the distinctive feature of “whites of the eyes.”

The white sclera in humans contrasts markedly with the pigmented skin surrounding the eye, and with the pupil, facilitating the detection of the orientation of the iris and the direction of gaze. In addition, humans have more of the sclera exposed (relative to face and body size) than do other primates, making the pupil (and direction of gaze) all the more conspicuous (relative to orangutans, the amount of visible sclera is two to three times larger in humans).

Since humans are heavily dependent on cooperative social interactions, and frequently engage in joint attentional interactions with others (in which gaze following may play an important role in coordinating the attention of cooperating individuals), selection may have favored a loss of pigmentation in the sclera as a means of facilitating social communication, an idea known as the “cooperative eye hypothesis.”

Interestingly, visible whites of the eyes are a feature of many domesticated dogs.

- from The Museum of Comparative Anthropogeny (MOCA)

("What?" by John Siskin)