After a little research, I have come to a more definite conclusion. According to the article, Baby's First Dreams from the American Institute of Physics, a 7 month old human fetus spends most of its time asleep. During sleep, they are cycling back and forth through states of rapid-eye movement (REM) and non-REM sleep. Since we know that humans dream during the REM state and that 7 month old fetuses experience REM, I conclude that babies do dream in the womb.
Steve Marshall, a self-help and spiritual writer claims to have personally recalled a couple dreams he experienced while he was in the womb. He was able to remember these dreams through the practice of Rebirthing, a New Age breathing technique. His article is titled Why Do We Dream. I don't know if there is anyone else that claims to remember their dreams, let alone any experience in the womb but I found this very interesting.
The next question to ask is: If babies can dream in the womb, what do they dream about? My guess is that babies dream about sounds they hear and things they feel and see in the womb. A baby is able to follow a flashlight moving across the mother's stomach, which means they can at least see different shades of things. Babies must dream about whatever they are sensing.
After writing my post on pregnancy & dreams, Pregnancy Brings Vivid, Real Like Dreams I'm surprised this question never came to mind. I'm glad someone asked me because I am obsessed with dream research and meaning!