If worrying is so natural and has so many survival advantages (See my article Why Worry?), you may say, why not worry? The short answer is that it is well enough to worry for short periods when the crisis requires it, but it is unhealthy and unproductive to get into the habit of worrying all the time.
First there is the physical impact of worrying, which is only slightly less than being terrified. Part of the fear response that goes along with worrying is the release of hormones that prepare the body for fight or flight. Although these hormones are great for helping you escape deadly situations by fighting or running like mad for short periods of time, a steady dose of these hormones is harmful over the long haul. Increased release of cholesterol, for example is good for intense fighting or running situations, when your blood pressure skyrockets and your capillaries spring tiny leaks. Cholesterol plugs these tiny leaks and prevents massive bruising. But if your cholesterol level is up all the time, the stuff can clog your coronary arteries and lead to heart attacks as we all know from the studies on heart disease among type A personalities who are good at worrying a lot.
Another physical effect of fear is the redirection of blood flow from the gastrointestinal tissues to the large muscles of the arms and legs, on the assumption that you won't be stopping for a bite to eat while fighting or running for your life. So the digestion of worriers is adversely effected, leading holistic medicine guru, Andrew Weil, to comment that whenever he hears of a GI complaint, he thinks of emotional causes first.
Finally, the higher blood pressure that goes with chronic stress punctuated by episodes of panic can lead to headaches and an increased risk of stroke or aneurism.
When our big brains evolved to allow us to worry, our life spans were in the 25 to 35 year range, so the adverse health effects of stress may not have killed us any sooner than the wolves would have. But now that we look forward to a few golden years beyond the 65th, the effects of chronic worrying and stress have time to accumulate and give us something else to worry about.
There are also mental consequences of slipping into the natural habit of worrying a lot. Nothing focuses the mind like the prospect of being hanged in the morning, to paraphrase Dr. Johnson - or eaten in the night, as our ancient ancestor B-rock might have put it. Fear causes us to remember the scary stuff so that we don't forget to avoid it the next time it shows up. This is useful for critical dangers, but it can have the effect of riveting our attention on a problem in such a way that our creativity is compromised and our appreciation of everything else that is going on is nearly obliterated. It is as if we have blinders on and can't see anything but the danger, even if the danger is imaginary or highly unlikely.