I thought it was pretty much ubiquitous to have to license pets throughout the US.
Both my dogs and cats have Hillsborough County licenses (well the cats had one, because I only renew them when I take them to the vets.) When I lived in AK I needed Municipality of Anchorage licenses for all my dogs, but I could purchase a Kennel license that covered them all. Like a contractor pack at Home Depot. Licenses are generally cheaper if the dog is fixed as well.
As an anecdote I found a loose dog in my neighborhood several months back with just a county tag on, and I was able to call Animal Control, give them the license number, and they gave me the phone number listed for the owner, so I could get the pup home.
ETA after I saw Declaration Day's post: the only enforcement I've ever seen in FL is if your pet ends up in the pound, you'll need a valid license to get it back. I can't imagine our officers going door to door.