A phobia is "a persistent, irrational fear of a specific object, activity, or situation, that leads to a compelling desire to avoid it' (dictionary.com).
I came across this listing of types of phobias on http://www.phobia-fear-release.com/types-of-phobia.html.
Among those, the common ones would be acrophobia (listed as altophobia) (heights), arachnophobia (spiders), claustrophobia (confined spaces), etc.
I thought there were more common ones?