Here's a funny one:
Cats suck the breath from sleeping infants.
I think this myth is hilarious because it is so wrong. The myth most likely came from people not knowing what SIDS was in the old days, and wanted to blame SOMETHING to make themselves feel better, even just a little bit, so the cat was a good culprit.
I don't know if this has ever happened, if so it's very rare, but the only way that a cat would smother a baby is if the cat smelled milk on it's mouth and wanted to lick it off, or by cuddling with the baby. If the cat smells the breast milk/formula on the baby's mouth and decides it would also enjoy a taste, it might sit on the baby's chest and lick their mouth. If the baby is too young it turn itself over or can't move because of the weight of the cat, it might be possible for the cat to accidentally cause the child the stop breathing. The cause of death would be from the cat's body being heavy enough to compress the baby's chest so much that it couldn't take in any new air.
The cat getting into the crib to cuddle and sleep next to the baby because it's warm and soft might possibly cause death from the cat's body covering it's mouth and nose so it can't breathe. That would also only be possible if the baby is young enough that it can't roll over or move it's face away.
My cat Munch is very protective of our son Lucian. He will sleep in Lucian's bedroom and they play together every day. Munch watches over our son like he is the baby's keeper or something! It's so sweet.
Here is a picture of Munch sitting close to Lucian after he fell asleep in the living room. He got tired after playing with all of his toys, which are scattered everywhere! The other two are them playing together.