I never had any problems with my cat and babies. To be honest, it horrifies me that people think animals are expendable objects just because it doesn't suit you to have them anymore. Sure, things need to change when a baby comes along, but you need to change your husband's habits when a baby comes along too and no one would suggest you have him put down!

As for issues with cat diseases (I think its toxoplasmosis?), I was told that it is highly likely that you have already been exposed to the disease if you've had puddies for any length of time, and that you have no cause for worry. I still didn't take the chance, and my DH dealt with kitty litter when I was pregnant - just as well given I had morning sickness for 9 months, let alone any disease risk.

Dogs are a different deal to cats though. I wouldn't be comfortable leaving any dog unsupervised with a baby, no matter how well the dog had proved himself to be of good character in the past.