Jungian psychological types are probably the most widely used and amongst the best-known in everyday life. Jung's typology emerges from Jung's deep, holistic philosophy and psychology about the person. Jung's typology is not, unfortunately, always included in mainstream personality courses, because it wasn't empirically-driven. Jung viewed the ultimate psychological task as the process of individuation, based on the strengths and limitations of one's psychological type.
Myers-Briggs developed the Myers-Briggs Type Indicator, a commercially available questionnaire, which is widely used in business and training, etc. and which provides information and exercises for better understanding one's own personality type and others with who the individual interacts and works.
Keirsey has renamed and reconceptualized the Jungian types, but they relate very closely to the Jungian types. Keirsey refers to "temperaments" rather than personality.
Underlying all these typologies are four personality traits (functions):
Extroversion (E) --- Introversion (I) Do you recharge your energy via external contact & activity (Extroversion) or spending time in your inner space (Introversion)?
Intuition (N) --- Sensing (S) Do you rely on your inner voice (Intuition) or observation (Sensing)?
Thinking (T) --- Feeling (F) When making decisions, what do you rely most on? Your thoughts or your feelings?
Judgement (J) --- Perception (P) Do you tend to set schedules and organize your life (Judgement), or do you tend to leave the options open and see what happens (Perception)?
Using the letters above, it is possible to have a unique 4 letter code to indicate each of the 16 Jungian personality types, e.g., I am an INFJ.
Here is a quick questionnaire to check your own personality type.