People saying they never brake for animals are probably over-egging the pudding a bit.
Each situation varies. If I'm by myself on a country lane at night, and have spotted some rabbits early, I'll ease off and be prepared to slow if they shoot into the road. If I'm going more quickly down a straight and there's a car behind, I probably would only ease off.
For bigger animals, such as badgers or deer, I'll almost always brake - they can do some quite serious damage.
As a rule, I won't swerve though. If the road conditions allow, I'll position the car in the middle of the road say, if there's a deer standing on the verge looking like he might run across. When it comes to braking hard though, you don't want to be steering at all.
If someone's tailgating me, I'll already be driving more slowly to take account of the fact they're close behind - so hopefully no rear end collisions. I may show my brake lights at the first sign of an animal to give them extra warning that I might be slowing.
And to those who say you might lose control of the car whilst braking hard to avoid an animal - you're going too fast!