Who can dream? Of course most of human beings dream, even they cannot remind the contents, we experience the imaginary world. Does this happen in animals? Probably if you ever had dogs, you might see many times when your dog is dreaming.
copied from: http://www.storm.ca/~townson/photos/sleeper.jpg
But how about cats? How about rats or mice? Maybe yes, maybe not? According to my experience, I think rats also dream. Same as dogs, they have spatial memory so that they can eat food from same location; they have episodic memory so that they can expect when they can eat food after doing a typical task. As you may know, we can have classical conditioning. That process involves those episodic memory and also spatical memory.
Dreaming can be expressed as a way ones brain remind something they saw, memorized, even a sudden image or sound they saw, heard, etc. While we are sleeping, brain does not stop working. Even brain activity may reduce than when one's awake; however, brain cannot stop working. Because input of information to the brain still remains. One information stimulates a group of neurons, and those neurons transfer the information to others. It is theoretically possible that eventually the brain attenuates and stop processing the information; however, as long as we can hear, see, feel gravity, pain, etc; always some kind of input exist while we are sleeping.
As long as one have his/her consciousness, it is probable that one can see dream. When you see a dream, you might feel you are in the real world and once you awake, sigh with relief knowing a horrible dream was not real. Why do we feel the dreams are real? I think it's because some higher function area in our brains (possibly any of frontal lobe areas) where can judge reality is not as much active as awake when we sleep. Even rats brains are not as much Hi-Tech as ours, they have consciousness as same as humans; they feel hunger, fear, excitement, familiarity, etc. So I think it is possible that rats dream.
Someone saw a rat dreaming?
Now, how about insects? Hmmm... Good question; however, according to the logic I said above, it may be possible because they also have brains.
Personally, I have seen many dream that I am conscious that it is dream and I can start controlling what happens next. Usually, in good ways, for instace, even I am in seriously terrible situation, I can survive from the tragedy.
If we stop dreaming, possibly we also stop seeing yellow flower garden when one is just going to die.