We just published a new paper investigating personality types in large datasets (>1.5M respondents) finding robust support for at least four distinct personality types.
M Gerlach, B Farb, W Revelle, LAN Amaral
A robust data-driven approach identifies four personality types across four large data sets
Nature Human Behaviour (2018)
A non-technical summary (+video) can be found at Northwestern News
Some news coverage:
Science News
Time Magazine
Washington Post