UPDATE! With the legislation of Companies Act 2014, effective 1st June 2015, any companies registered from this time as the new Private Company Limited by Shares (LTD) may have a minimum of one director.
Companies Registered before 1st June 2015, must either convert to the new LTD or another type of company (i.e. DAC) and once this is done may have a minimum of one director.
Please note that if there is a single director, this person cannot also serve as Company Secretary, so another person must take on this role or you must have a second director.
A minimum of Two Directors are required to incorporate a private limited company (the most common trading entity). There are proposals in the Companies Consolidation Bill 2012 to reduce this requiremnet to One Director but this will not take legal effect until later this year.