Not all that common. From what I've heard about heavy set dogs are used, like bull terriers - a dog with strong jaws that will latch on to a pig and not let go, until someone steps in to slash the pigs throat with a "pig sticker" (knife). You can buy leather neck protectors for the dogs.
Probably still goes on today. In many states here hunting is not allowed in state forrests so some people will use dogs like this to minimise any noise and chances of getting caught. I came across one of these hunting parties while 4 wheel driving through a state forest in Western Australia many years ago - their 4wd ute with dog cage was parked off the side of a track.
