It is recommended to request a rehoming fee to discourage bad people from doing bad things with the animal. A pet should never be “free” because it not only draws in people who may not be financially capable, but this is one way people obtain animals for dog fighting/baiting (amongst other terrible things.)
Taking an animal to a shelter or rescue is a much better solution. I think most people go the craigslist route because they are concerned of them having a time limit, or there is something about the pet that would make them unadoptable.