The previous answer notes that an anarchical society provides the most freedom because there is a complete absence of a government imposing restrictions on personal conduct. As the question specifies a “system of government,” however, I would suggest that a democratic system guided by libertarian principles would provide the greatest level of personal freedom. Libertarianism is defined by its emphasis on the least possible government and the maximum possible freedom, both personal and economic. In a sense, it shares common principles with each of the two major political parties, the Republicans and the Democrats. It shares with Republicans an emphasis on minimal government intrusion in the marketplace, and it shares with Democrats an equally minimal government intrusion into the personal lives of citizens, such as their belief in personal choice on the issue of abortion.

A democratic system, including one outlined as a representative democracy such as exists in actual democratic systems around the world, provides the greatest degree of personal freedom. The citizenry elects its representatives, or, in a pure democratic system, votes on most or all matters individually. A democratic system guided by libertarian principles goes a step further by minimizing the size and reach of government. You can, as is the case in the United States, have a democratic system with a large and powerful central government. You can also, however, have a democratic system with very strictly proscribed authorities. Some US citizens believe that this was the principle behind the 10th Amendment to the US Constitution. That, however, is a matter for each individual to consider.

When debating types of government, the level of freedom that citizens enjoy is somewhat in the eye of the beholder.  I suppose the form of government that would provide people the most unlimited version of freedom would be anarchy, which is to say no government at all.  If there were no government (according to an anarchist) then there would be no government constraint... perfect freedom.  Now that said, anarchy has obviously never taken root in an entire society.  So, for my money, I would say that a direct democracy offers its citizens the most freedom.  The citizenry votes on each measure that the government deals with... in other words, the citizens have ultimate freedom of choice, for example in ancient Athens.