This article is from the Problem Behaviors in Cats FAQ, posted to rec.pets.cats newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
Cats can become jealous upon the arrival of a new baby. Reassure the cat that you still love it by paying it plenty of attention. In the exhaustion and turmoil of a new baby, the cat is often neglected, and this will add to its resentment.
There is a myth that cats will kill babies. The superstition is that they'll "steal" the baby's breath; the latter day explanation is that they will lie on babies and suffocate them. While cats may like the baby's warmth and may curl up next to it, it will not often lie on the baby and in any case will move when the baby begins to flail its arms and legs.
Most cats are trustworthy around babies after getting over any jealousy, especially if it is trained not to use people as toys; however babies should never be left unsupervised around any animal.