For instance here are seven different and largely incompatible, or at least mostly non-overlapping, schools of thought in psychology from around the late nineteenth / early twentieth century:

• Wundt's original approach, called voluntarism: the investigation of the nature and composition of mental states with an emphasis on the creative organizing and synthesizing abilities of the will
• Titchener's structuralism: the descriptive analysis of conscious mental states and their elements through the use of introspection
• functionalism, making no distinctions between the approach of its founder William James, the Chicago school, or other functionalist approaches: an approach based on the notion that mental capacities, like physical traits, evolved for an adaptive purpose and served important functions in human (and animal) life, rather than viewing the mind as merely a static collection of experiences
• behaviorism: the focus on observable organismic responses to environmental stimulus conditions, to the complete neglect and exclusion of the study of consciousness or the use of introspection
• Freud's psychoanalytic school, based on his own clinical observations and their implications for the development of personality and treatment of mental "disease"
• Gestalt psychology: an approach born in Germany around 1913 in opposition to structuralism, and which moved to the U.S. in the 1930's where it opposed behaviorism -- in both cases because it viewed psychological phenomena such as perception and behavior as consisting of inherently organized integrated wholes that couldn't be broken down into artificially identified components such as sensations, or stimuli and responses, or reflexes
• clinical psychology: not in the present-day sense of diagnosis and therapy for mental illness, but rather a collection of practices broadly construed to include psychometric approaches to measuring individual differences, intelligence testing and theorizing about intelligence, educational psychology, and applied psychology such as aptitude testing in the workplace and other contexts

Some other possibilities that you might come across:

• act psychology, a sort of German pre-functionalism associated with Franz Brentano in the 1870's and 80's
• the Wurzburg school led by Oswald Kulpe in opposition to some of the claims of Wundt and/or Titchener; in particular they claimed imageless thought was possible
• psychophysics, which studies the relationship between physical stimuli and correlated sensory experiences, associated with the work of Gustav Fechner and Ernst Weber in the mid-nineteenth century
• the physiological study of psychology's perceptual and biological bases, associated with Helmholtz, Mueller, Donders, and other in the nineteenth century
• early approaches to subject areas in psychology such as developmental psychology and even industrial psychology (the latter associated with Hugo Munsterberg)

For comparison (and curiosity) here is the list Edna Heidbreder considered in her history of psychology called Seven Psychologies in 1933.

• Titchener's structuralism
• William James's functionalism
• the Chicago school of functionalism
• behaviorism
• the Columbia approach called dynamic psychology (perhaps broadly functionalist)
• Gestalt psychology
• Freud's psychoanalytic school

Here is a brief description of the advent of the "college major" in the first decade of the twentieth century, from the Wikipedia entry on then-Harvard-president Lawrence Lowell:

In 1909, he became president of the American Political Science Association. That same year, he succeeded Charles William Eliot as president of Harvard University, a post he held for 24 years until his retirement in 1933.

Harvard reforms

Lowell immediately embarked upon a series of reforms that were both academic and social in nature. Under his predecessor, Charles W. Eliot, Harvard had replaced the single standardized undergraduate course with a system that allowed students free choice of electives. That was a logical extension of the trend in U.S. education that had modeled the university on the German system and thus adopted the German principal of student freedom in choosing courses. So dominant was Harvard's role in American education that all large American colleges and universities had adopted the elective system by 1904. It appealed to all student types, those intellectually curious and energetic as well as the lazy without intellectual ambition.

Lowell now implemented a second, equally revolutionary restructuring of undergraduate education. As early as his service on an ad hoc faculty Committee on Improving Instruction in 1903, he had determined that the elective system was a failure. Large numbers of students, lacking intellectual ambition, chose their courses with little concern for learning, more intent on the ease with which they could fulfill the course requirements, resulting in a course of study that was "neither rigorous nor coherent." Lowell dismantled the elective system and in its place established concentration (what is commonly call a "major") and distribution requirements that would soon become the new American model. Paired with the concentration requirement was a tutorial system in which every student had the guidance of a tutor to see he was prepared for examination in his area of concentration.