Most people do not. The condition is called pathological height vertigo. http://www.ptjournal.org/cgi/content/abstract/85/5/443

When I searched acrophobia this is what I found. Please read the information on the link entirely for a full understanding of the condition described in your question. . 'Causes Traditionally, acrophobia has been attributed, like other phobias, to conditioning or a traumatic experience involving heights. Recent studies have cast on this explanation;[1] fear of falling, along with fear of loud noises, is one of the most commonly suggested inborn or non-associative fears. The newer non-association theory is that fear of heights is an evolved adaptation to a prehistory where falls posed a significant danger. The degree of fear varies and the term phobia is reserved for those at the extreme end of the spectrum. It has been argued by researchers that fear of heights is an instinct found in many mammals, including domestic animals and human beings. Experiments using what are known as "visual cliffs" have shown human infants and toddlers, as well as other animals of various ages, to be reluctant in venturing onto a glass floor with a view of a few meters of apparent fall-space below it.[2] While an innate cautiousness around heights might be helpful for survival, an extreme fear can interfere with the activities of everyday life, such as climbing up a flight of stairs or a ladder.' . http://en.wikipedia.org/wiki/Acrophobia#Causes

I don't.