We have skunks, they usually are not a problem. One recently has gotten a liking of chicken. Killed one of my prized girls pre-dusk. I'd closed the coop in waning light and didn't discover her in corner of pen until opening it in morning. Four days later it came back after I'd let chickens out. Asked one daughter to grab my gun as I ran out to stop it from killing the rooster. Literally had a hatchet in hand and scooted the skunk out with it...was so tempted to break it's spine right then and there but didn't want to be sprayed. By the time my gun got to me it had ran behind neighbors shed.
Now he and I have our pellet guns handy and are awaiting it to show it's head in daylight again. My gun is 1100 fps and his is .22 caliber pellet.
Coon, possum, skunk, weasel, coyote, fishercat, grey fox, red fox and various raptors, pretty much in that order. The birds get a "pass" as protected species, the rest are free to roam the woods AWAY from the coop, but when they come near it's "game-on." Various traps and a .17HMR thin-out the ones that come too close.
We have plenty of Packrats here. They don't bother the chickens, but can wreak havoc particularly under the hood of motor vehicles. They have been known to cause literally thousands of dollars of damage overnight in a single car as they will chew through electrical wiring, hoses, not to mention the horrific stink they leave behind. You'll drive through RV campgrounds noting every car and truck's hood up. That will discourage packrats from building a nest around the motor.
Anyhow, I use a Hav-A-Heart trap baited with peanut butter and send them to see their Grandfathers with .22 LR birdshot. A couple of years ago I dispatched over thirty in one season.
Racoons, fox, possum, coyote, skunk, mink, weasel, hawks. By far, the racoons have been our biggest problem. We trap them and kill them. My husband shot mink last Spring that had a growing interest in coming around our chickens. We're lucky we saw him!
Coyotes, I fence them out and leave them to deal with the abandoned dogs and cats, rabbits, and other small pests
Eagles, hawks, and owls. None of which have shown an interest so I leave them to deal with mice and sparrows
Great Horned Owl. I have covered runs for at night so he can't reach the birds.
Raccoon. I know they are there, but they haven't been around. It is easier for them to eat the neighbor's cat food. My night runs are raccoon proof. The coyotes are happy to keep the raccoon population regulated.
Cougar. He lives about a mile from my house but does not appear to be interested in ducks or geese. He would not be able to break into my night runs.
Crows have killed a couple of chickens and 2 ducks and stolen dozens of eggs. I go after them with a shotgun. It makes them more cautious, but they still send a scout to do a flyover every morning. I haven't actually shot one of them, but I would if I could get close enough.
Loose dogs generally don't last more than 24 hours See "coyotes" above.
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.
Foxes, coons, and coyotes are the only thing i've ever had problems with. We have lots of other critters here but they don't cause issues. Snares work wonders for foxes and i've even snared 2 coyotes. The coons always knock down the snares. I caught a coon in my rabbit shed the other night eating eggs in the corner and i lit him up with my .22. My favorite predator control is a mossberg 12 gauge loaded with Hevi-shot dead coyote rounds. Drops them dead at 50 yards.
I have a live trap set but all i ever catch is sable my rabbit, chickens, and i caught a baby opossum twice. The first time i caught the opossum i released it because it was not causing issues, the second time i caught it, i relocated it about 15 miles away because i was worried if it ever became a problem i'd never be able to live trap it again because i caught it twice already.