Coyote, fox, possum, skunk, racoon, weasel, birds of prey, roaming dogs....
My solution: My birds sleep in a very, very secure coop. They have a covered run for when I need them penned up. Their coop/run has access to a securely fenced pasture where they can "free range". I also use hot wire around my pens to discourage predators. We have plenty of hawks hunting the hayfields all around us, they've never shown an interest in my birds. But my birds have easy access to duck into the barn just in case.
Coyotes are my biggest problem. They can't get to my birds but I don't care to loose my good barn cats to them. When they get brazen and start roaming around near the house/barns in the daytime they get shot. I don't do any trapping of smaller critters, don't need to. BIrds are locked up securely at night, no food is accessible at all. I also have a couple of dogs that discourage predators from snooping around much.