Yes, research and testimonies of blind people say that they do infact!

Dreaming makes your recall memories that may be visual, auditary, olefactory, touch or taste. 

We have visual dreams, because a large part of our memory is filled with visual images. 

However, the memories of blind people are stored with inputs from other senses.

These memories are often connected with emotions, and blind people experience them too.

Infact, research says that

1) If a person was blind from birth he hardly has no visual impressions in his dream. He may however, for example : dream that he is walking around the house touching the furniture as he goes by and he feels happy that his children have come home, by hearing their voices.

2) If a person lost his sight during his lifetime, the amount of visual information in his dreams will depend on when he lost it. A person who lost his sight before 5 years may hardly have any visual dreams when he reaches 40. However, a person who lost his sight 5 years ago will still have vivid visual perceptions in his dreams.

This group of people may infact create visual memories through touching and feeling objects which they later recollect during dreams as visual perceptions.

This question has an analogue to animals like snakes , bats which have very poor or no sight. However, it has been researched that even the most primitive animals like fish experience REM sleep.