Fear is a very useful evolutionary trait. Species have survived for millions of years simply by running away at the slightest hint of a threat. Considering how useful fear can be, it comes as no surprise that mother nature occasionally deals out an overdose, which we humans recognize as anxiety, nervousness, or neurosis.
Animals can be neurotic, too. Just as humans bite their nails, some Dobermans have a nervous habit of chewing on their paws. A recent genomics study examined these paw-chewing Dobermans, and found that they tended to have a special version of one gene called CDH2. This appears to be a bona-fide behavior gene, a kind of holy grail in the field of behavioral genetics.
In humans as in dogs, inbreeding may permit neurosis genes to rise to the top and manifest themselves. For instance, I have been told that the Baba Nyonya, a group of Chinese-Malays who traditionally marry within the family, suffer from a high degree of mental illness among their females. Similarly, some researchers are studying whether certain neuroses are overrepresented among Ashkenazi Jews, thus explaining the ouvres of Woody Allen and Larry David.
Although fear might be useful from an evolutionary standpoint, too much of it can be crippling, and can even result in unnecessary violence. As Yoda put it, fear is the path to the dark side. Ultimately, neurosis/fear/anxiety are products of not only nature, but also nurture. We can't easily control our genes, but by diversifying our social interactions we can distinguish true enemies from those who exist only in our heads - a step towards a less anxious and less stressful life.