The big five personality traits are the best accepted and most commonly used model of personality in academic psychology. The big five come from the statistical study of responses to personality items. Using a technique called factor analysis researchers can look at the responses of people to hundreds of personality items and ask the question "what is the best was to summarize an individual?". This has been done with many samples from all over the world and the general result is that, while there seem to be unlimited personality variables, five stand out from the pack in terms of explaining a lot of a persons answers to questions about their personality: extraversion, neuroticism, agreeableness, conscientiousness and openness to experience. The big-five are not associated with any particular test, a variety of measures have been developed to measure them. This test uses the Big-Five Factor Markers from the International Personality Item Pool, developed by Goldberg (1992).
Carl Jung (1875-1961) was Swiss psychiatrist who proposed a theory of psychological types. His theory was taken and extended by Katharine Briggs and her daughter, Isabel Myers, personality enthusiasts who had studied his work extensively. They developed the Myers-Briggs Type Indicator which classified people into 16 different types on the basis of four dichotomies:
3. Thinking-Feeling, and
The first three were adapted from Jung and the last developed by Myers-Briggs. So, for example, a person could be Extroverted-Sensing-Feeling-Perceiving (ESFP) or Introverted-iNtuiting-Thinking-Judging (INTJ). The Myers-Briggs types are the most popular pop-psych system. The Open Extended Jungian Type Scales was developed as an open source alternative to the Myers-Briggs Type Indicator
The roots of DISC was a book published in 1928, titled Emotions of Normal People. In it, William Marston theorized that a person would express their emotions in one of four ways, from which come the four letters D I S C. He did not intend to make an assessment, though, and modern DISC does not have all that much in common with Marston's work. In the 1950s a series of industrial psychologists separately used his theory as the basis of a tool for employee selection and organization. Today there are many tests that exist under the name DISC, marketed by various psychological consulting companies for use by human resources departments, each with their own differences.
British psychologist Raymond Cattell found that variations in human personality could be best explained by a model that has sixteen variables (personality traits), using a statisical procedure known as factor analysis. Following this discovery he went on to create and promote the 16PF Questionnaire. This test uses a public domain scales from the Internation Personality Item Pool to measure the same traits.
All of these tests are provided for educational and entertainment uses only. They are not clinically administered and as such the results are not suitable for basing important decisions off of. These tests are also not infallible, if the results say something about you that you don't think is true, you are right and it is wrong.