Yes, and we can even make an educated guess as to what they dream about: Elephants.
All mammals have REM sleep, the same as we have when we have vivid dreams. The animals, like us, have a small cluster of cells that turns off the muscles when dream sleep begins. Scientists have disabled this function in some animals and watched them act out their dreams. The activity that dominates during dreams depends on the type of animal. Rabbits scan for danger; cats hunt; rats explore.
As far as I know, no such experiment has been conducted on elephants. But we can infer their most likely dreams based on their ecological niche. Elephants are not predators, and have only moderate trouble with predators other than humans. They are highly social animals, and their relationship to the group is important for their survival. (Lone elephants do have predator troubles.) Long lived, social and intelligent, the species they most resemble is humans. And humans dream mostly about humans.
