New experiments suggest that rats might (the only definitive answer would be for one to tell us!) dream. By monitoring the brain activity of rats under three scenarios: 1) food visible, but not reachable. 2) Asleep after viewing food that was not reachable and 3) when the rats finally walked to the food. The regions of the brain associated with walking and navigation were active in all three scenarios. This suggests that much like during our sleep, when the hippocampus is processing thoughts/observations for memory, the rats may also be dreaming of a tasty treat.
When rats rest, their brains simulate journeys to a desired future such as a tasty treat. Researchers monitored brain activity in rats, first as the animals viewed food in a location they could not reach, then as they rested in a separate chamber, and finally as they were allowed to walk to the food. The activity of specialized brain cells involved in navigation suggested that during the rest the rats simulated walking to and from food that they had been unable to reach.
http://www.sciencedaily.com/releases/2015/06/150626083433.htm