I've been fascinated for years (all right, decades) with the Kiersey Personality Sorter. It was based on the MMPI, which is a comprehensive test, something like 600 questions. The MMPI is used a lot in dealing with mental illness, but for people trained in what to look for it tells a lot more about the people taking it than they would ever dream.
The Kiersey is much shorter and has many practical uses. They give it to department heads at work. There are no right or wrong answers to the questions, but merely give insight into how the taker views the world.
You can find my March 21st post here where I provide an overview of it, and my March 28th post here where I discuss Introverts vs Extroverts. I'll take the series up again in May.
I'm an EXFP -- you'll have to check out the March 21st post to see what that means.
What is your personality type?