If you're planning on having kids, or are already pregnant and you're thinking of getting a dog or cat, don't. Just plain don't do it. Wait until the baby is born and a little older. I love all of our animals, but they are a LOT of work and when it comes to priorities in our house, the baby always comes first. This means that the dogs don't get walked every day and that the litter boxes don't get scooped as often as they should. But most of all, it means none of the animals get the attention they deserve. Having a child is all-consuming. It leaves you with very few spare brain cells. I'm not saying you can't have pets and kids at the same time, but that if you can be pet-free during the newborn stage, your life will be a little easier. You're about to embark on a brand new adventure with a tiny human. Save the adventure with your furry friend for a time when you can focus.
Also, when picking a new pet for your family, do your homework. Read up on different breeds of dogs and cat and find one that will suit your family's personality. German Shorthaired Pointers are known for being amazing family dogs, but they are VERY energetic and can easily knock over a child in their enthusiasm. We know this, and have taken the appropriate precautions. Don't just wander down to the shelter one day and pick the first dog that strikes your fancy. You will have this dog for the rest of its life, so make sure you can live with it.
Okay, for those of us who already have pets and are unwilling to give them up: It's okay. Like I said, we have 2 dogs and 5 cats and it's fine. We didn't let any of the animals anywhere near the Eskimo for the first couple of months, but as he got older, there wasn't much we could do to prevent them from hanging out. One of our cats absolutely loves him. She sits next to him and will actually carry a feather wand over to him so he will play with her. But he's a grabby little boy and often will end up with a fist full of cat hair and an angry cat. Do NOT leave your pets alone with the baby. I don't care how much you trust your animals. They are animals and that is not their baby. In their eyes, it's just another tiny creature in the house vying for your attention. Supervise all interactions, watch for cues that your pet is getting stressed and intervene when necessary. The Eskimo loves nothing more than pulling on our dogs' ears, but if they're not in the mood, I let them walk away. I never keep one of our pets near the baby if they don't want to be there. I want nothing but happy thoughts for them when they're around him.
The supervision thing carries over into naptime and bedtime as well. I can't supervise pet/baby interactions at night. I don't let any of our animals into the baby's room, at all. It would probably be fine, but we've all heard horror stories of cats smothering babies and that is NOT going to happen in my house. Plus, it's a lot easier to keep the nursery clean without pet hair in it.
We've had a really good experience with our pets and our baby. We've not had any problems, yet. Just pay attention and do your best to set your pets up for success.