Is it the one that looks like an actual luggage tag (that you can put a picture or something in) or is it one of the new tags with a train or a steamship on it? Either way, I leave them both on. I've put pictures of my dog in the luggage tag type ones. The new ones with the train/steamship are works of art that absolutely are left on my bag!
Those tags on some of the bags that just say it's made of deerskin get yanked off and tucked into the inside pocket. I know some people leave them on, but I don't care for that at all.