We have a flock of red tailed hawks that nest in our neighborhood. They generally keep a block or two away, but sometimes come visit my chickens. If they are free ranging, and the hawks swoop by, my roosters will send a warning call out. All the chickens, roosters and hens both, will run to cover.
They are strangely defensive when it comes to wild doves. If they fly over, the roosters will make a call that I've decided means: "don't run yet, but know that something's up". I've also watched them run at doves that land in the yard.
My roosters are all silkies or seramas, and are as gentle as they come, but very protective of their girls. They each have their own little group of hens. If another rooster tries to mate with their hen, they will challenge him and chase him off.