A dream is a series of images, ideas, emotions, and sensations which generally happen unwillingly in the mind in certain stages of sleep. Dream is dependent on the condition and situation of the human beings in their life. If an individual is a student then he dreams for good marks. If a person is jobless and unmarried then he dreams for job and married life so the examples make it clear that the mostly dreams are dependent on the situation of life of a person. Some people see unexpected dreams related witch or other types.
Dreaming occurs during Rapid Eye Movement (R.E.M) sleep which most mammals also experience. The director of Evolutionary Neurobehavioral Laboratory at Boston University says that as mammals experience REM sleep, it is reasonable to suppose that animals have some thing like we call dreams.
Scientists and experts are not sure that animals sleep. Many pet owners have seen their sleeping dogs or cats pull jaws with sudden jerk as if they are seeing eatable thing like bones or mice. After about twenty minutes a dog enters REM sleep which is the stage of dreams. Experts say big dogs sleep longer. Little dog sleep quickly and frequently. Insects and fishes do not experience REM sleep.
In short it is yet to find out whether animals dream like us.