Bureaucracy has three principal meanings in contemporary social science. In the tradition established by Max Weber the term refers to an ideal type of rational authority and rule-based organization, as compared to traditional or charismatic authority and organization. Weber's original frame of reference was the Prussian (and later, German) civil service.  In this sense, the typical government agency, nonprofit organizations like the American Red Cross, and large business corporations are all bureaucracies.
In political science, terms like "the bureaucracy" and "the federal bureaucracy" or "state bureaucracy" largely embrace the Weberian meaning and add an additional connotation of systems of formally or rule-based coordination between distinct or distinguishable organizations typically composed of more than one organization.  In this second sense, the full set of national-level government agencies, together with their state and local subsidiary offices are all included in the term federal bureaucracy.
In a sense widespread in contemporary U.S. politics but ultimately attributable to the Austrian economist Ludwig von Mises, the term bureaucracy is often used to refer primarily or exclusively to pejorative aspects of government organization: dysfunctional behavior, rigidity, apparently foolish lack of common sense, lust for personal power, and other similar characteristics. Ludwig von Mises captured this connotation in his 1944 book, Bureaucracy with the phrase "the opprobrious connotation of the term bureaucracy". In the first paragraph of the introduction, he wrote:
The terms bureaucrat, bureaucratic, and bureaucracy are clearly invectives. Nobody calls himself a bureaucrat or his own methods of management bureaucratic. These words are always applied with an opprobrious connotation. They always imply a disparaging criticism of persons, institutions, or procedures. Nobody doubts that bureaucracy is thoroughly bad and that it should not exist in a perfect world.
The abusive implication of the terms in question is not limited to America and other democratic countries. It is a universal phenomenon. Even in Prussia, the paragon of authoritarian government, nobody wanted to be called a bureaucrat.
However, von Mises added, those who attribute the misfeasance of government to bureaucrats, miss "the point as it makes bureaucracy and the bureaucrats responsible for an evolution the causes of which must be sought for elsewhere. Bureaucracy is but a consequence and a symptom of things and changes much more deeply rooted."
- Weber, Max. Economy and Society: An Outline of Interpretive Sociology. Translated by G. Roth and C. Wittich. New York: Bedminster Press, 1968.
- See for example, Woll, Peter. American Bureaucracy. 2d ed. New York: Norton, 1977.