Italians seem to have a much more progressive attitude towards pets (especially dogs) than Americans do. I have been told that most of Europe is like this. You will find many store owners that bring their dogs to work, and a lot of Italians will take them to lunch as well. The only restriction seems to be that you can't bring a dog into an actual restaurant, but rather have to eat on the patio (which is very common). Also, I don't remember any dogs trying to eat off of the table or even expecting any table scraps.
I'm not sure if this is a causation or correlation, but the dogs also seem to be better behaved here as well. I only heard 1 dog bark the entire trip, and I don't remember a single dog trying to chase after the numerous cats that populated the streets. Also, at least a quarter of all of the dogs that were out for a walk with their owners were not leashed, but stayed in close proximity to the owners anyway, rarely venturing more than 10 feet away to sniff something or check someone out.
The only drawback I saw to this is some irresponsibility of the owners. Specifically, you will find dog poop on the sidewalk at least once every few blocks. I imagine this is similar to other concrete jungles, as there is no place for the dog to go except on the pavement. This doesn't excuse the owners from cleaning it up, but I suspect that the percentages between here and the US are similar for dog owners that don't clean up after their dogs, the only difference being it is more noticeable here because there aren't really any grass strips for the dog to use.