I guess we are lucky here in the UK. We do have that worst of 2 legged predators ie man, but natural predators are less of a problem. I guess the only one that ever used to bother was not even a predator as such in that adders bite in defence not to try to eat the dog but it could still be fatal (I imagine you have problems with venomous snakes elsewhere was well). However in the last few years there has been a growing problem with foxes - especially in the urban areas becoming aggressive towards small dog breeds and cats not to mention humans. As was observed about coyotes I consider a major cause of this to be a change in attitude from aggression towards them to "leave nature alone". Unfortunately this is not going to do foxes any favours in the long run - they are being forced into an ecological niche nature did not intend them to inhabit, that of apex predator.
I think people need to start understanding that man is part of nature too and while he should not be randomly and massively killing things neither he be failing to defend himself against them. There is a world of difference between paying a bounty on every head no matter how killed - trap poison gun, and limited killing of only those animals which become a problem.