The MBTI (Myers-Briggs Type Indicator) is a self-assessment and self-discovery instrument for Psychological Type. It was developed in the late 1940s and has been in use since the 1960s. To date, millions of people have taken the MBTI. The questions have been reconsidered and rewritten multiple times, based on how well they sort people into "Type". The assessment currently in use is "Form M".
Notwithstanding its popularity (or perhaps because of it), there are detractors. One of the loudest of these, Adam Grant, bases most of his dislike for the MBTI on the fact that he has gotten inconsistent results. In other words, he interprets his ability to "trick" a self-assessment tool, by supplying different answers each time, as a flaw in the tool. (I lost any respect for Mr. Grant after reading his essay on the topic.)
Another common method of refuting the MBTI is a version of what techies call "Not Invented Here" syndrome. Simply put, the creators of the MBTI were not psychologists.