Fear is such a huge part of rabbits' lives that they even have a word for a special type of fear they feel: Tharn, meaning paralyzed with fear (5.14). (If this were an American book, we'd expect a rabbit-version of FDR to give the speech about only tharning tharn itself.) Of course, if you were a rabbit too, you might be afraid, since just about anything can kill you—humans, disease, other animals, cars, a mean look, etc. So rabbits need some level of fear to survive from all the dangers they face. But fear can itself be part of the problem if they become too paralyzed to act, which happens a fair few times in Watership Down.
As cheesy as it sounds, fear can be overcome through teamwork in Watership Down.
Fear always leads to bad things for the rabbits.