There are many varied opinions surrounding the topic of cats and newborn babies. Every year a huge number of cats are surrendered to shelters because a new baby is on the way or has arrived and the parents worry about the risk the cat poses to the child. Most shelters are desperately overworked and underfunded and this just adds to their burden. During my own pregnancies, I was told by several well-meaning people that I would have to get rid of my cats once the baby arrived. People are very fearful of cats smothering babies, however, despite a great deal of time trawling the Internet for information, I was only able to find two cases, one a conflicting story of Kieron Johnson, who was purportedly smothered to death and one in a near miss, as covered in the British Medical Journal. 
Keeping baby safe:
It goes without saying new parents need to take precautions. You can purchase a net to put over the crib so the cat can't sleep with the baby. Another good suggestion is to replace the door to the baby's nursery with a screen door. This enables the cat to see and smell the baby and not feel entirely left out, but it can't get into the bedroom.
Make sure litter trays and food bowls are kept in an area the baby can't access, this is especially important when the child starts crawling. A safety gate is recommended to prevent your child getting close to the litter tray.
Ensure your cat is regularly de-flead and de-wormed. Make sure the products you use on your cat are safe to use around the baby. If you are worried about your cat scratching your baby, (which is highly unlikely), you can either regularly trim your cat's claws (see trimming cat's claws), or use Soft Paws, which are plastic caps you glue over your cat's claws.
Can a newborn baby be around cats?
Yes, it is fine for a newborn baby to be around cats as long as they are supervised. A cat should never be allowed to sleep next to a baby, but both can quite happily reside in the same home. In fact, there is a lot of research to suggest that children brought up with pets in the first year of their life have a lower incidence of allergies later on.
Other myths surrounding cats and babies:
One common myth is that cat's suck the baby's breath. This is untrue. If a cat is found close to the baby's head it's more likely due to the cat seeking some warmth. If the above suggestions are followed, this won't happen.
Cats harbour disease:
Cats sometimes do harbour disease but there are very few diseases of the cat that are zoonotic (transmissible from cat to human). It is fairly rare to pick up a disease from a cat, personally, I believe you (or your baby) are far more likely to catch a disease from another human than a cat (our daughter had to be rushed to hospital as a two week old after catching a cold from a family member). It is recommended that you take your cat to the vet for a thorough check-up before your baby is born. Have the vet worm your cat and check him for ringworm. Ensure you stick to a regular worming and de-fleaing regime. Keeping your cat indoors and away from roaming cats is your safest way to keep your cat disease and parasite free. It is probably a good idea not to adopt a kitten at this time.
Toxoplasmosis is caused by a parasite called Toxoplasma Gondii. Many animals can get toxoplasmosis including sheep, cattle, and pigs. Cats shed the parasitic cysts in their faeces and which then infect humans and other animals.
In healthy adults, toxoplasmosis usually causes only mild symptoms. If a woman becomes infected during her pregnancy it can have devastating affects on the unborn fetus. If you own a cat and are pregnant it is advisable to ask your doctor to do a blood test to see if you have antibodies to Toxoplasmosis, which would indicate a past exposure to the parasite. If you have been infected in the past, there is little to no risk of you passing it on to your unborn baby. If you haven't had prior exposure it is advisable to have your partner clean litter trays during your pregnancy. If this is not possible, use rubber gloves and try to avoid inhaling any dust from litter trays, it is advisable to wear a mask. It takes between 24-48 hours for the cysts to become infective, so daily cleaning of the litter tray will almost entirely eliminate the risk of infection. It is perfectly safe for pregnant women to co-exist with their family cat as long as these precautions are taken.
Humans can also become infected by handling (and eating) raw or undercooked meat and vegetables. Ensure your meat is thoroughly cooked and that you wash your hands and utensils after handling meat. There is a greater risk of you becoming infected with Toxoplasmosis from raw and undercooked meat than there is from your cat if kept indoors.
Ringworm: This is caused by fungi, not a worm. It is more a nuisance than a danger. It can sometimes be hard to eliminate from the environment, however, with stringent cleaning and the use of anti-fungal creams it is can be cleared up. Again, if your cat is indoors and has had the all clear from your vet, there is little chance of you or your baby catching this. Ringworm is more common in kittens and cats living in overcrowded conditions.
Rabies: Rabies isn't a problem in Australia. Most (if not all) cats in countries with rabies regularly vaccinate their cats, it is very rare for a cat to catch the disease.
Cat Scratch Disease: This is caused by a bacteria called Bartonella henselae. This is rarely a problem in people with a healthy immune system, it is most often seen in immunocompromised people. Antibiotic treatment of you and your cat usually clears up this infection.
Salmonella: Caused by a bacteria of the Salmonella genus. This is most commonly acquired via oral ingestion. Cats are most likely to become infected after eating birds.
If you still have any doubts about raising a baby with a cat in the house I would recommend you speak to both your vet and your doctor who will be able to put your mind at ease.
During my pregnancy, I spoke to several mothers who all assured me they had quite safely managed to raise cats and kids together and had no problems whatsoever. The people who warn you that cats and babies can't co-exist are always people who haven't actually researched this matter. They just repeat urban legends.
Cats and new babies can co-exist together quite happily but your child's safety has to be of utmost importance. NEVER leave a baby or young child alone with any pet, cat included.
Cats and humans have lived together for thousands of years but it is important to remember that they are still wild animals and their behaviour cannot be predicted with 100% accuracy. A cat should never be permitted into the same room a baby/young child is sleeping and proper safety precautions should be taken to ensure the cat doesn't have access to the baby's room.
If proper safety precautions are taken to ensure your cat and baby/young child are only together under adult supervision your cat and child will be able to quite happily cohabit together and hopefully once the child grows older will form a long and lasting bond.