Psychoanalysis was founded in the 1890s by the Viennese physician Sigmund Freud. Freud was the first to seriously explain the way in which behaviour is determined by the unconscious mind. Freud has been criticised, perhaps rightly so, for a one-sided obsession with sex as a determining factor in shaping the nature and development of the psyche. Later depth psychologists, like Adler, Jung, Reich, and Horney, in various ways tried to correct the shortcomings and to go beyond the limitations of Freudís work
Carl Jung accepted the theory of libido, but de-sexualized it, associating it with "psychic energy" or "life force". Jung eventually founded his own movement of Analytical Psychology or Archetypal Psychology, based on the concept of the Collective Unconscious.
Alfred Adler replaced sexuality with feelings of inferiority as the primary factor. According to this, one starts out feeling weak and being dependent upon adults for survival; developent is a struggle or striving for superiority to overcome these feelings of inferiority.
Anna Freud was Freud's daughter and the founder of child psychoanalysis. She also developmed the theory of defense mechanisms, which protect the ego from the disruptive influences of unconscious wishes. These include four processes: displacement, projection, rationalization, and reaction formation.
Karen Horney founded the American Institute for Psychoanalysis, and developed a theory of neurosis and feminine psychology
Wilhelm Reich went from psychology to paraphysics, when his investigation of energy functions in human emotions led to the discovery of what he called orgone energy (equivalent to ch'i or prana). This was too much for the conservative establishment; the American FDA followed the lead of Nazi Germany and burned his booksPsychoanalysis seems to sit strangely with the rest of secular western understanding. While Reich's work is considered psedoscience in a knee-jerk manner [although see this detailed critique for a better coverage], and Jung is seen as sitting dangerously close to the mystic (ditto Ken Wilber, another bridge-builder between academia and the ancient wisdom traditions), the work of Freud himself, as well as Anna Freud, Karen Horney, and others, remains respected.
Psychoanalytical Psychology - good intro
Psychoanalysis - short but good basic entry