Many OB-GYNs mistakenly inform their patients that they must get rid of their cat or cats in order to ensure the safety of their unborn child. This is not at all true. This misconception is based on fear of a parasitic disease called toxoplasmosis, which can be transmitted from a variety of sources to a pregnant woman and can be dangerous to her fetus. Cats are exposed to this parasite through the ingestion of live prey (e.g., mice), and it can then be passed on by the cats to humans through handling the cats' feces, which most commonly occurs during litter box cleaning.
However, assuming cats are indoor animals (i.e., not catching live prey), there is no danger that a pregnant woman or her unborn baby will contract the parasite from the cat. In fact, pregnant women run more risk of exposing their baby to toxoplasmosis by handling raw or undercooked meat in their kitchen than by handling their indoor cat.
That said, as a precaution, it is best for another family member to be responsible for litter box cleaning during the pregnancy (and good practice, since after the baby is born, Mom is certain to have her hands full and this task may need to be permanently reassigned) or, alternatively, for the mother-to-be to wear gloves and wash her hands thoroughly after cleaning the box if she must do it herself. Pregnant women should also use caution when gardening in outdoor areas that may have been used by strays as an open-air litter box.