Do unborn babies cry? Yes, they do.
As Dr. David Chamberlain explains, "The emotional turmoil which provokes crying already exists in the womb and may be heard if air reaches the area around the fetal larynx. This intrauterine crying is termed 'vagitus uterinus' (literally, squalling in the womb) and is well documented in medical literature both ancient and modern."
Apparently fetal crying can be audible when air is present in the uterus (which is rare). But even without air, the fetus can perform exactly the same crying motions as a born child, just without sound.
A 2005 study suggests that unborn children can cry in the womb by 28 weeks gestation, and perhaps as early as 20 weeks.
Researchers led by Jeannie L. Gingras, M.D., concluded in the Archives of Disease in Childhood -- Fetal and Neonatal Edition: "The fetus is capable of responding to sound and other perturbations with highly coordinated movements that mimic temporal and behavioral components of the extrauterine cry. These observations may have further developmental implications, as the expression of crying implies more than execution of a motor pattern."
The Discovery Channel has an ultrasound video of an unborn child crying here.