Cats

First of all, you can have a cat and a baby. Doctors even today caution women against having a cat and a baby, but it is safe. Here the top concerns:

1. Toxoplasmosis - If you have a spouse, its his job to clean the litter box for the next 9 months. If you live alone, you are either going to have to beg someone else to come clean if for you, or you are going have to wear gloves and a mask each time you do it. Either way, cat boxes are no more dangerous than gardening or handling raw meat.
2. Smothering the baby - You can train your cat to not go in the crib or bassinet even before the baby comes home. We didn't need to do this, but I'm sure that it isn't all that different from training your cat not to do anything else. If your cats are anything like ours, then once the baby is home, they won't be all that interested in snuggling up anyway. Besides, if you room in (like is suggested to reduce the risk of SIDS anyway) then you will be able to keep closer tabs on how close your kitty pal is getting. When you aren't in the room, then you can keep the baby's room closed to keep the cat out.
3. Allergies - Having a cat in the home doesn't mean your child will get an allergy to cats. My daughter is closing in on two, and she shows no signs of an allergy to cats. And, both my husband and his brother grew up in a home with multiple cats and neither of them has an allergy to cats. If you are still worried, just be extra diligent about cleaning up fur and dander. Vacuum more frequently. Put baby down on a play blanket instead of the carpet (which I always felt better about anyway). Lint roll your clothes after you have a kitty snuggle.