The least complex animals with ability to dream
Since mammals all share the same neural structures it is quite likely that most non human species dream, but as yet, the simplest animal I could find that has been scientifically demonstrated to dream is the rat, as proven by Massachusetts Institute of Technology (MIT).

MIT not only established that rat were capable of dreaming about the events they had experienced while awake, but that the content of the dreams could be manipulated with audio cues the rats had been trained to respond with in a specific way.

Sources:

http://en.wikipedia.org/wiki/Brain#Mammals

http://web.mit.edu/newsoffice/2012/neuroscientists-achieve-dream-engineering-0902.html