Pets

When introducing your child to animals caution is the greater part of valor.  If you already have a pet don't leave your infant alone with them.  Your fresh baby may, to a dogs point of view, seem reminiscent of a squeaky toy or a prey animal.  If you have a cat remember that your baby is made of warm, and you expect your cat to not sit on the stationary warm thing in a bassinet? Even if your pet is friendly and intends no harm, baby animals are cared for in a way that is not compatible with human babies.

When first introducing a small child to a pet (yours or someone else's) it's important to teach your child how to touch softly /slowly/ nicely.  You don't want your child to provoke a pet.  What do you expect an animal to do if it feels threatened?  Your child might not be much of a threat, but does an animal know that?  Different animals have different temperaments.

Your results may very, and adult supervision is required.

My son gets very excited whenever my mom comes over with her miniature poodle.
"Dogdog!"  (the name by which most of the animal kingdom seems to fall under at the moment for my son)
Last time my son saw this little dog he grabbed the leash and walked around the living room with her. Though as my brother pointed out it was hard to tell who was walking who.

When we visit my sister and her cat, that cat has time and again had the good sense to keep clear of our small human.  We also intentionally kept my son out of the room with the litter box in it.  I don't even want to deal with the idea of my son ingesting a super absorbent sand-like material that may or may not currently contain cat excrement.

Pet food dishes are also problematic.  These dishes live on the ground for easy access to the pet.  But small children with more curiosity than sense may take an interest in these as well.  Even if your child does not try to consume the pet food, playing and making a ridiculous mess with the pet food could easily be a thing if steps are not taken to actively prevent it.

Pet birds can be fun too, as long as you keep small fingers from poking into the cage.  Aquariums and terrariums can be fun to look at and fairly safe too as long as they stay out of reach of children too young to stay out of trouble.