We have about 100 birds and at any given time two or three will be broody. We collect the eggs everyday so sometimes the broody hen will just sit there on nothing or on one of our "fake" eggs (we put fake eggs in the places we want the hens to lay their eggs). We'll remove the broody hens from the coop several times a day until we break them of the habit. That usually works.
Occasionally we'll have snakes get into the coop and eat eggs. If the snake gets a porcelain fake egg that pretty much the end of that snake eventually. Rattlesnakes are more difficult, but we've gotten pretty good had removing those, too.
Our big problem this year is hawks (our chickens free range). We've lost about 20 birds this year just to hawks. Just this last weekend hawks killed three (flew away with two and mostly maimed a third I had to cull) and one hen got away missing her tail feathers and received some deep cuts our vet stitched up. She got away because our dominate rooster attacked and killed the hawk after her.