Direct democracy is a straw-man, easily knocked down, because it is difficult to coordinate across large numbers of citizens, even with modern technology. On top of that, most of us are too busy working and raising families to follow all the issues closely enough to make informed votes on policy options.
There are no countries governed by direct democracies. Outside the U.S., the closest example of direct democracy is Switzerland, which has some limited aspects of direct democracy. The closest examples to direct democracy in the U.S. were the town hall meetings held in some parts of Colonial New England.
Excerpted from America: Republic or Democracy.
Image: Rauthaus (Townhall), Basel, Switzerland.
 The New England town hall meetings were generally not true direct democracies because voting rights were assigned only to men who owned property and who were members of the local church. See Lockridge, Kenneth (1985). A New England Town. New York: W.W. Norton & Company. ISBN 978-0-393-95459-3.