While it's not the same type of burial humans hold for one another, some chimpanzees and elephants have been known to put leaves and branches over members of their groups that have passed. Mourning has also been observed in other animals such as dolphins, horses, cats and dogs.
When a member of an elephant herd dies, the herd will visit the body, poking and touching it with their trunks and feet. Much later when they return they will stroke the bones of their fallen friend. Dolphins act in a similar way, guarding the body of their dead for days. House pets like cats and dogs have been known to wail and act in a depressed manner when one of their companions dies.
This is not to say that these animals understand death, or that they can anticipate it in a companion that is suffering from a disease. What scientists can say is that animals understand and feel loss and grief the same way they feel joy and sorrow.