The Big Five or Five-Factor Model is a theory of personality types that has become accepted by mainstream psychologists. If nothing else, it is more discussed than such rivals as the MBTI ("Big Four"?) and the Enneagram ("Big Nine"?).
It states that there are five main dimensions of human personality:
These five dimensions should be understood as continuous, as the four MBTI dimensions ought to be. [psychologycharts.com] shows how the Big Five traits relate to other theories of personality. For the MBTI, Extroversion carries over, Openness is Intuiting as opposed to Sensing, Agreeableness is Feeling as opposed to Thinking, and Conscientiousness is Judging as opposed to Perceiving. Neuroticism has nothing corresponding to it in the MBTI.
I've seen several theories of what subtraits there are, and also a theory of supertraits with associated neurotransmitters [crystalknows.com] :
[gosling.psy.utexas.edu] extends this work to other species, finding that Extroversion and Neuroticism go back a long way.