Geese can often deal with domestic dogs, but will sometimes fall victim to more wiley predators (like coyotes), but will make a racket if anything is going on (and often when nothing is going on). I've heard of people using swans for poultry protection animals - swans are nasty. I've heard people using Guinea fowl as alert/lookout animals, but my understanding is that foxes/coyotes eat them just as easily as chickens - it's just louder.
The best is a well trained livestock guardian dog of the proper breed. The tough part is that "well trained" thing, as a poorly trained LGD can be a nightmare.
My chickens and ducks range between two pastures - the back pasture has some sheep and a llama. The front pasture has a quad of geese - the front pasture is essentially my backyard, so I worry about it a little less.
Both pastures are fenced and hot. Multiple layers.