The answer to this question ultimately depends on what your definition of spying is. If we are to go by the standard definition of spy, which is referrd to as secretly watching the movements and actions of other people, especially an enemy for ulterior motives, then I'll say that governments do not spy on individuals.
Government activities which revolves around collecting individual informations is aimed at better securing it's citizens by searching and flushing certain individuals which are on a watch list and pose possible immenent threat to the society. Asides from this, i doubt any government has more reasons to spy on it's law abiding citizens are they are not the enemies.
However, there has been many conspiracy theories which are official unconfirmed on government activities revolving around the needless spying of it's citizens. One of such situations was the case with the American whistle blower, Edward Snowden. He came forward with proves of how the government uses illegal surveillance techniques to spy on the public. Although the American government at first denied the accusations, they later claimed the program was aimed at monitoring certain individuals which were believed to pose certain threats to the society.