How comfortable are you letting your baby or young child play with a pet?

I see videos on youtube of babies playing with dogs and cats which involves climbing onto them, pulling their fur, crawling around them. I always think you can never trust an animal. My dogs are my babies and I can pull food out of their mouth and they don’t do anything but they have snapped at me once or twice.

Do you have pets and babies that play together? If so, how did you introduce them to each other? Do you always feel the need to supervise them? Do they always play good?

If you don’t have babies and/or pets then what is your view on this?