Babies love playing peekaboo because they don't have object permanence; they don't realize that objects still exist when they are out of sight. Between 8 and 12 months of age, babies begin to develop a sense of object permanence, and subsequently become bored of playing peekaboo.
In this study of object permanence in dwarf goats, researchers find that these ungulates are able to track the movements of (and find) a concealed treat (uncooked pasta). Dwarf goats are clever; a past study found that they are also able to use indirect information to find a food reward (a test that sheep fail). That is, when shown two cups -- one with food, one empty-- the goats select the "food" cup whether they are shown the food or the lack of food in the "wrong" cup. So seeing no food in cup A leads them to infer that cup B must contain the hidden reward, a relatively advanced cognitive task.
Perhaps most interestingly, dwarf goats demonstrate the ability to understand open-ended categories. So if you give goats examples of shapes, some of which lead to food rewards and some of which do not, they are able to generalize observed patterns into "rules" for novel shapes. If all of the food-associated shapes are black with white centers, the goats know to prefer a novel black shape with a white center over a novel black shape without.
Pygmy goats are also well-known for their habit of riding horses (video).
Dwarf goats have more in common with young children than you might think: adorable faces, ear-piercing screams, and now object permanence—the understanding that things still exist even when they disappear from view. The ability typically develops in humans between 8 and 12 months of age; it’s the reason peekaboo never gets old for babies. Previous studies have shown that other animals such as dogs, cats, and various primates reach different stages of object permanence, but a new study is the first to investigate its existence in the tiny ungulates, researchers will report in the June issue of Applied Animal Behaviour Science.